Ali is the point where Islam divides, and the division is about events, not doctrine, which is why it has never been argued away.
He is the Prophet's cousin, raised in his household, married to his daughter Fatima, and father of Hasan and Husayn. Both Sunni and Shia tradition agree on all of that, and on his being among the earliest to accept the message. They diverge on what happened in 632.
Sunni tradition holds that the community gathered at Saqifa after the death and gave allegiance to Abu Bakr, that this was a legitimate consultation, and that Ali eventually accepted it and became the fourth of the Rightly Guided Caliphs. Shia tradition holds that the Prophet had already designated Ali at Ghadir Khumm, on the return from the farewell pilgrimage, taking his hand and saying that whoever holds me as his master holds Ali as his master. The event at Ghadir Khumm is reported in Sunni collections too, including chains Sunni scholars accept; the dispute is about what the word rendered master means. Shia read it as authority and designation. Sunni read it as friendship and support.
So this is not a case of one side inventing an episode. Both accept the report. They read one Arabic word differently, and a fifth of the world's Muslims stands on each side of the reading.
Ali became caliph in 656 after the murder of Uthman, faced civil war, and was killed in 661 at Kufa by a member of a faction that had abandoned him for accepting arbitration.