Why did the Companions side with Aisha in the Battle of the Camel, but not with Fatima when she demanded her inheritance from the Messenger of Allah from Abu Bakr?

The Companions - may Allah be pleased with them - are the best generation in this nation. If they differed on a matter, they would strive and seek the truth diligently, as happened between Fatimah and Abu Bakr - may Allah be pleased with them both - regarding inheritance. Fatimah - may Allah be pleased with her - exerted her effort (ijtihad), and the correctness was with Abu Bakr - may Allah be pleased with him - due to the Prophet’s saying, peace be upon him: "We do not inherit; what we leave is charity."

As for the Battle of the Camel, it was a tribulation in which the face of truth was hidden from many Companions. So, they went out seeking retribution for the blood of the Commander of the Faithful, Uthman - may Allah be pleased with him. Among them was Aisha - may Allah be pleased with her - while many of them were with Ali - may Allah be pleased with him, and others withdrew from the tribulation. The Companions - may Allah be pleased with them - were mujtahideen (those who exert their effort to derive legal rulings). So, whoever was correct receives two rewards, and whoever erred receives one reward for his ijtihad.