It is not permissible for one who is fasting to insult anyone
Committing sins during the day in Ramadaan, such as swearing or insulting others, does not invalidate the fast as such, but it detracts from the reward for fasting. These sins may take away all of the reward, and the fasting person is left with nothing as a result of his fast apart from hunger and thirst.
The fasting person is enjoined to guard all his faculties against disobeying Allaah. The purpose behind fasting is not simply to refrain from eating and drinking, rather the purpose is to refrain from disobeying Allaah and to achieve piety or fear of Allaah. Allaah says (interpretation of the meaning):
“O you who believe! Observing As-Sawm (the fasting) is prescribed for you as it was prescribed for those before you, that you may become Al-Muttaqoon (the pious.)”
The Prophet (peace and blessings of Allaah be upon him) said: “Whoever does not give up false speech and acting upon it, Allaah has no need of his giving up his food and drink.” Narrated by al-Bukhaari, 1903, 6075.
False speech includes all kinds of speech that are haraam, such as lying, backbiting, slandering, insulting and cursing.
And the Prophet (peace and blessings of Allaah be upon him) said: “If any one of you is fasting, let him not utter obscenities or act in an ignorant manner, and if anyone insults him or wants to fight him, let him say, I am fasting.” Narrated by al-Bukhaari, 1894; Muslim 1151.
“Let him not utter obscene speech” means let him not say any foul words.
“Let him not act in an ignorant manner” means let him not do any of the actions done by ignorant people such as yelling, being foolish, etc.
What is meant by this hadeeth is that he should not react in kind, rather he should limit himself to saying, “I am fasting.”
If the fasting person is commanded not to react to one who insults him, how can it be appropriate for him to mistreat people or be the first to insult them?
Note that the prohibition against obscene speech, ignorant action, argument and insults on the part of one who is fasting is not restricted only to him, rather each of these things is forbidden in general, but the prohibition is stronger in the case of one who is fasting.
Al-Haakim narrated that Abu Hurayrah (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Fasting does not just mean abstaining from food and drink, rather fasting means abstaining from idle and obscene speech. If someone curses you or treats you in an ignorant manner, then say, ‘I am fasting, I am fasting.’”
Ibn Maajah (1690) said: Abu Hurayrah said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “It may be that the fasting person gets nothing from his fast apart from hunger, and it may be that the one who prays qiyaam at night may get nothing from his qiyaam but a sleepless night.”
See also Question no. 37989 concerning lying whilst fasting.