What is the truth behind the dispute that occurred between Ali and his wife, and Umar and Aisha, may Allah be pleased with them?

There was no disagreement among the Companions regarding doctrine or the methodology of deduction. Rather, their relationship was based on love and intermarriage, as Umar married Umm Kulthum, daughter of Ali and Fatimah, and Al-Hussein named his sons Abu Bakr and Umar. The dispute that occurred between Fatimah and Abu Bakr was concerning the inheritance of the Prophet, peace be upon him, where Abu Bakr informed her that prophets do not bequeath inheritance, which he had heard from the Prophet. Abu Bakr had no personal desire in this matter, and he also prevented his daughter Aisha from inheriting.

Ali delayed pledging allegiance to Abu Bakr for six months after the death of the Prophet, peace be upon him, due to the death of Fatimah and his desire to consult the Companions regarding the caliphate. When Fatimah passed away, Ali pledged allegiance to Abu Bakr after he was reassured of the correctness of Abu Bakr's stance on the inheritance. Bukhari and Muslim narrated this matter, and Ali was not an opponent of Abu Bakr or one who broke the unity of the Muslims. Ali's delay in pledging allegiance was not a disparagement of it, for it is not required for every Muslim to pledge allegiance to the Caliph in person. Fatimah's avoidance of Abu Bakr was not an unlawful boycott, but rather a reluctance to meet him, and Ali agreed with her in her withdrawal due to her grief.

Umar was known for his strength and firmness, which made some fear his presence, while Abu Bakr was gentle. Ali affirmed to Abu Bakr that he did not envy him for the caliphate, but he reproached him for his autocratic handling of the matter without consulting them. Abu Bakr affirmed to Ali that the kinship of the Prophet, peace be upon him, was dearer to him than his own kinship, and that his stance on wealth was in accordance with the Prophet's Sunnah. This incident vindicated everyone, and it became clear that the hearts of the Companions were united in respect and love, despite the human differences that may occur.