What was the reason the Prophet, may God's prayers and peace be upon him, forbade Ali from marrying the daughter of Abu Jahl, despite her embracing Islam and her father's death? And was there a justification for prohibiting that permissible matter?

A Muslim must submit to what has been authentically reported from the Prophet, peace and blessings be upon him. Polygyny is permissible in Islamic law, but it may be prohibited if it leads to greater harms than benefits, such as the inability to act justly. From this perspective, the Prophet, peace and blessings be upon him, prohibited Ali ibn Abi Talib from marrying another woman while married to Fatimah, may Allah be pleased with her, for several reasons: harming her would harm the Prophet, fear for her faith due to jealousy, disapproval of the daughter of the Messenger and the daughter of the enemy of Allah being simultaneously married to one man, and out of reverence for Fatimah's right and status. These reasons, collectively or individually, were the cause of the prohibition. The story does not mean that polygyny is forbidden in general, for the Prophet, peace and blessings be upon him, said: "Indeed, I do not forbid what is lawful, nor do I permit what is unlawful."