What was the reason the Prophet prohibited Ali from marrying the daughter of Abu Jahl while he was married to Fatimah, and does that go back to the Messenger's refusal that they be gathered in one house or with one man?

The Prophet, peace and blessings be upon him, rejected Ali's marriage to the daughter of Abu Jahl while he was married to his daughter Fatimah, not out of fear of them living together in one house, but for the reason he clarified in his sermon: "I do not forbid what is lawful, nor do I permit what is unlawful. Indeed, Fatimah is a part of me; what troubles her troubles me, and what harms her harms me. And I fear that she may be tempted away from her religion. However, if the son of Abu Talib wishes to divorce her and marry the daughter of Abu Jahl, then by Allah, the daughter of Allah's Prophet and the daughter of Allah's enemy shall never be united under one man." So, Ali abandoned the proposal.