Why did Prophet Mohammed (saws) not let Ali marry another woman?

Question

"An indication of their special relationship is found in the fact that Ali never married another woman as long as Fatima was alive. Sunni sources explain this curiosity in a tradition in which Ali asks for Abu Jahl's daughter in marriage, but the Prophet does not allow him to marry her because it would upset Fatimah."
Denise L. Soufi, "The Image of Fatima in Classical Muslim Thought," PhD dissertation, Princeton, 1997, p. 51-52

I cannot understand why Prophet Mohammed did not let Ali to marry another woman while Islam gives permission to a man to marry four wives? If Fatimah can be upset so every woman whose husbands marry more than one wife can be upset, right? When God allows men to have four marriage, why Prophet Mohammed said no?

Answer 1

The Prophet (peace be upon him) prohibited `Ali from being married to his daughter and the daughter of Abû Jahl at the same time. He said:

“The daughter of Allah’s Messenger will not be together with the daughter of Allah’s enemy.”

It can be understood from the context of this hadîth that the Prophet (peace be upon him) had placed a condition on 'Alî not to marry any other woman beside Fâtimah. We can deduce this from what the Prophet’s (peace be upon him) said about his other son-in-law (Abu Al-'As bin Ar-Rabi', the husband of his daughter Zaynab) keeping his promise not to marry a second wife: “He spoke to me and he was truthful and promised me and fulfilled his promise.”

Ibn Hajr observes in Fath al-Bârî (7/86):

The words “He spoke to me and he was truthful” could be that he made a promise on himself not to marry another woman beside Zaynab. And the same was done by 'Alî. Otherwise, it could be that 'Alî had forgotten that condition and that is why he proceeded with that engagement to the second woman. Or, it could be that he assumed the condition did not apply to him since he did not pronounce it himself. However, he should nevertheless have respected this condition as something understood, and that is why the Prophet (peace be upon him) blamed him.

Ibn al-Qayyim writes in Zâd al-Ma`âd (5/117-118):

If a man agrees to the condition that he will not marry a second wife, he is obliged by that condition. If the man breaks his promise, the woman will be entitled to terminate the marriage contract.

It is mentioned in the hadîth that what took place is hurting Fâtimah and therefore hurting him. It is known for sure that the Prophet (peace be upon him) let 'Alî marry his daughter Fâtimah on the condition that he does not hurt her or her father, even if that is not mentioned in the marriage contract. The Prophet (peace be upon him) brought up mention of his other son-in-law to incite 'Ali to do the same.” The Prophet’s reproach of `Ali was on account of 'Alî’s heedlessness of this condition.

And Allah knows best.

Source: Implicit condition not to marry a second wife

This is the Sunni view.