She received a marriage proposal from someone who is infertile and her family rejected him
Infertility is one of the faults that affect marriage according to the more correct of the two scholarly opinions. This has been discussed previously in the answer to question number 121828.
The suitor has to disclose it, and the woman to whom he proposes has the right to accept him or reject him. If she accepts him with this fault, she does not have the right to request an annulment later on because of not having children. If she does not know about the fault and then finds out about it after marriage, she has the right to ask for an annulment if she does not accept the fault.
Ibn Qudaamah (may Allaah have mercy on him) said: One of the conditions of having the option to annul the marriage because of these faults is that one should not have had knowledge of them at the time of the marriage contract and should not have accepted them afterwards; if the person knew of them at the time of the contract or came to know of them afterwards and accepted them, then he or she does not have the option of annulling the marriage contract, and we do not know of any scholarly difference of opinion concerning that. End quote from al-Mughni, 7/142.
Having children is a blessing and is one of the aims of marriage, so a woman should not marry a man who is sterile or infertile unless she knows that it is possible for him to be treated and recover.
If your family are rejecting the suitor, then they are excused for that. Undoubtedly they are seeking your best interests and striving for your happiness.
If you think that this suitor is appropriate for you, because of his good character and religious commitment and because it is possible to treat his infertility, then you have no choice but to convince your family to accept him. If you manage to do that than praise be to Allaah; but if they insist on their opinion, then they are excused as stated above, and perhaps Allaah will send you someone who is better than this suitor.
It is well-known that marriage is not valid without a wali or guardian, because the Prophet (blessings and peace of Allaah be upon him) said: “There is no marriage without a guardian.” Narrated by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Maajah (1881) from the hadeeth of Abu Moosa al-Asha’ri; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
And he (blessings and peace of Allaah be upon him) said: “Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid.” Narrated by Ahmad (24417), Abu Dawood (2083) and al-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami, no. 2709.
We ask Allaah to guide and help you.
And Allaah knows best.