We can answer this one who is objecting or is confused by mentioning a number of basic matters which must be borne in mind in order to understand this topic and examine it: 

Firstly: 

There is nothing in existence but it has some similarities with other things, even in some general aspects. Man is similar to inanimate objects in that both exist and are created. He is similar to animals in many ways – both of them are living creatures that eat and drink, and live and die. In fact philosophers define man as “a talking animal.” 

Similarly, there are many similarities between man and plants, in that both of them are alive and grow and need nourishment, and so on. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

No two things exist but there must be some similarity between them in some way, even if it is a very subtle similarity. To suggest that there is no similarity at all (between any two things that exist) is like suggesting that they do not exist. No such notion has ever been narrated from any wise man or thinker.

End quote from Bayaan Talbees al-Jahamiyyah (7/569) 

It is not known that any wise man or thinker ever regarded any of the similarities mentioned above as something reprehensible in man that deserved to be criticised and condemned. They are similarities which are either praiseworthy or are physical similarities that are subject to neither praise nor condemnation. 

Secondly: 

Comparing or likening, from a logical and linguistic point of view is based on four principles: the item being likened to something else, the thing to which it is likened, the aspects in which they are similar, and the words used to highlight this similarity.

If we ask about the ruling on a particular comparison and whether it is made by way of condemnation or of praise, then it is not right to limit our focus to the thing to which it is being likened. Rather we must also think of the ways in which they are similar. 

It was narrated from one of the Sahaabah that he likened his own action to the action of an animal, as ‘Ammaar ibn Yaasir (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) sent me on an errand and I became junub. I could not find any water, so I rolled in the clean earth like an animal.

Narrated by al-Bukhaari (347) and Muslim (368). 

No one understood this as meaning that he likened himself to an animal in all aspects in a blameworthy manner – Allah forbid – because from a linguistic point of view it can never be taken to mean such a thing. 

So it is essential to understand Arabic, which is the language of the Qur’an and Sunnah, before indulging in such baseless specious arguments, which are indicative of utter ignorance of Arabic style and usage. And it is essential to examine the ways in which the two things are similar, before making accusations that this likening is an insult to all women or is derogatory to womankind. 

Thirdly: 

The hadeeth mentioned in the question is the hadeeth of Abu Hurayrah (may Allah be pleased with him) who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Prayer is interrupted by a woman, a donkey and a dog, but something like the back of a saddle protects against that.” Narrated by Muslim (511). The one who reads this hadeeth will realise that the “likening” referred to here has nothing to do with the bad attributes of either donkeys or dogs, or that women are on the same level as these animals – Allah forbid. This is wrong thinking and a foolish notion. ‘Aa’ishah (may Allah be pleased with her) did not mean that at all when she heard this hadeeth and said: “Are you likening us to donkeys and dogs?”! Narrated by al-Bukhaari (514). 

Rather the similarity between them that is referred to here is their simply having a specific action in common that has to do with the prayer, which is distracting the worshipper from his humble focus and connection with Allah, may He be glorified and exalted. ‘Aa’ishah (may Allah be pleased with her) did not agree that the passage of a woman (in front of one who is praying) disrupts the humble focus of the worshippers towards Allah, may He be glorified, but many of the Sahaabah disagreed with her on that. 

We should point out that the basic principle about passing in front of a worshipper and the worshipper’s prayer being affected by the one who walks in front of him, no matter who the one who walks in front of him is – man or woman, human or animal – is that all of that (i.e., passing in front of one who is praying) is not allowed. The Prophet (blessings and peace of Allah be upon him) said, with regard to preventing anyone from doing this blameworthy action: “If the one who passes in front of the worshipper realised what there is (of blame and sin) on him, standing (and waiting) for forty would be better for him than passing in front of him.” Abu’n-Nadr said: I do not know whether he said forty days or months or years. Narrated by al-Bukhaari (510). 

Indeed, al-Bukhaari (487) and Muslim (505) narrated that Abu Sa‘eed al-Khudri (may Allah be pleased with him) used to pray on Fridays facing something that would screen him from the people. A young man from Banu Abu Mu‘ayt wanted to pass in front of him, and Abu Sa‘eed shoved him in the chest. The young man looked, but he could not find any way to get by except walking in front of him, so he tried again to pass in front of him, and Abu Sa‘eed shoved him harder than the first time. He said something bad to Abu Sa‘eed, then he entered upon Marwaan and complained to him about what Abu Sa‘eed had done to him. Abu Sa‘eed entered upon Marwaan after him and (Marwan) said: What is going on between you and your brother’s son, O Abu Sa‘eed? 

He said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “If one of you prays facing towards something that is screening him from the people, and someone wants to pass (directly) in front of him, let him push him away, and if he insists then let him fight him, for he is nothing but a devil.” 

An-Nawawi (may Allah have mercy on him) said: 

With regard to the words of the Prophet (blessings and peace of Allah be upon him), “for he is a devil”, al-Qaadi said: It was said that what is meant is that it is only the Shaytaan who made him pass in front of him and made him refuse to go back. It was also said that what is meant is that he (the one who wants to pass in front of the worshipper) is doing a devilish action, because the Shaytaan is far removed from goodness and acceptance of the Sunnah. And it was suggested that what is meant by the shaytaan here is the qareen (devil companion), as it says in another hadeeth: “for he has the qareen with him.” And Allah knows best.

End quote from Sharh Muslim (4/167) 

It is quite clear that this hadeeth is general in meaning and applies to anyone who wants to pass in front of one who is praying; this story of Abu Sa‘eed has nothing to do with women at all! 

Fourthly: 

Because passing in front of one who is praying is forbidden in all cases, and applies equally to men and women, and that also affects his prayer, some of the scholars are of the view that the passing in front mentioned in these hadeeths is to be understood as not rendering the prayer invalid and making it obligatory to repeat it. Rather what is meant is that it has an impact on its perfection and humble focus in the prayer, because it is a distraction that attracts the attention of the worshipper. 

Al-Qurtubi (may Allah have mercy on him) said: 

That is because a woman may be a source of fitnah, a donkey may bray and a dog may be frightening, and the one who thinks about that may become so distracted that his prayer is interrupted and spoiled. Because these things could lead to interruption of the prayer, they are described as interrupting it.

End quote from al-Mufhim lima ashkala min Talkhees Saheeh Muslim (2/109) 

Ibn Rajab (may Allah have mercy on him) said, after mentioning a similar interpretation: 

It would be more correct to say, instead of this interpretation: because the worshipper is focusing on conversing with Allah, and he is very close to Him, the worshipper is instructed to take precautions against the Shaytaan interfering in this private conversation and closeness to Allah. Therefore it is prescribed to use a sutrah (screen) to guard against the interference of the Shaytaan when praying, because, in this situation, he will try to interrupt the worshipper who is conversing with his Lord. As the Shaytaan is cursed and expelled far away from the Divine presence, if he comes close to the worshippers, that would lead to taking the worshipper away from his Lord and interrupt his conversing with his Lord. 

It is for this reason – and Allah knows best – that these three are singled out for taking precautions against them. They are: 

Women – because women are the traps of the Shaytaan, and when a woman goes out of her house, the hopes of the Shaytaan are raised; the Shaytaan sought to bring about the expulsion of Adam from Paradise by means of women. 

The black dog is a devil, as is stated in the hadeeth. 

The same applies to donkeys, hence one is to seek refuge with Allah when hearing the voice of a donkey in the night, because it has seen the Shaytaan. 

Hence the Prophet (blessings and peace of Allah be upon him) instructed the worshipper to draw close to the sutrah (screen), lest the Shaytaan interrupt his prayer. But that does not necessarily mean that the prayer is invalidated and must be repeated, and Allah knows best. Rather it detracts from the prayer, as was stated by the Sahaabah such as ‘Umar and Ibn Mas‘ood – as is mentioned above about a man passing in front of a worshipper: the Prophet (blessings and peace of Allah be upon him) instructed him to shove him and fight him, and he said, “for he is nothing but a devil”; according to another report, he said: “for he has the qareen with him.” But the interruption that is caused by the passing of these animals which are particularly associated with the Shaytaan is greater. This is what is meant by interrupting the prayer; it does not mean that it is rendered invalid and must be repeated. And Allah knows best.

End quote from Fath al-Baari by Ibn Rajab (4/135) 

Fifthly: 

It is unfair and unjust for a researcher, no matter what his religion or school of thought is, to deliberately quote a single, ambiguous report that is open to interpretation and has nothing to do with the topic he is researching, then use it to impugn a perfect religion that has a complete set of guidelines on laws and etiquette, such as the religion of Islam, whilst turning a blind eye to dozens of texts and teachings that honour women in that religion in such a way that they are not honoured in any other religion, law or legal system. 

It was narrated that ‘Aa’ishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Women are the twin halves of men.”

Narrated by at-Tirmidhi (113); classed as saheeh by al-Albaani in Saheeh Abi Dawood (234). 

Al-Khattaabi said: The words “Women are the twin halves of men” mean they are their peers and are like them in physical makeup and attitude, so it as if they are the twins of men. 

In terms of fiqh, this indicates that whenever something is stated in the masculine, it is also addressed to women, except in specific cases where there is evidence to indicate that they are exclusive (to men).

End quote from Ma‘aalim as-Sunan (1/79) 

The scholars quoted this hadeeth as evidence for the principle that what is obligatory for males is also obligatory for females, and what is permissible for males is also permissible for females, and there is no differentiation between them unless there is a text to that effect. 

Hence the Qur’an addresses women just as it addresses men, and there are many texts that indicate that, such as the verse in which Allah, may He be exalted, says (interpretation of the meaning):

“Verily, the Muslims (those who submit to Allah in Islam) men and women, the believers men and women (who believe in Islamic Monotheism), the men and the women who are obedient (to Allah), the men and women who are truthful (in their speech and deeds), the men and the women who are patient (in performing all the duties which Allah has ordered and in abstaining from all that Allah has forbidden), the men and the women who are humble (before their Lord Allah), the men and the women who give Sadaqat (i.e. Zakat, and alms, etc.), the men and the women who observe Saum (fast) (the obligatory fasting during the month of Ramadan, and the optional Nawafil fasting), the men and the women who guard their chastity (from illegal sexual acts) and the men and the women who remember Allah much with their hearts and tongues (while sitting, standing, lying, etc. for more than 300 times extra over the remembrance of Allah during the five compulsory congregational prayers) or praying extra additional Nawafil prayers of night in the last part of night, etc.) Allah has prepared for them forgiveness and a great reward (i.e. Paradise)”

[al-Ahzaab 33:35]

For more information, please see the answers to questions no. 70042, 40405 and 132959 

And Allah knows best.