Basra was laid out in the 630s as a garrison for the armies moving into Iran, with tribal quarters around a mosque and a governor's residence. Within two generations it was one of the places where Islam worked out what it thought, because a garrison city drew people from everywhere and gave them no inherited local authority to defer to.
Hasan al-Basri, who died in 728, is the figure everyone in the following centuries wanted to claim. He preached self examination, fear of God and detachment from the wealth pouring into the city, and later Sufi orders put him at the head of their chains of transmission. He also took a position on the question that divided early Muslim thought, whether human acts are created by God or by the actor, and the sayings attributed to him hold people answerable for what they do rather than assigning their sins to divine decree.
Traditional accounts derive the Mutazila from a dispute in his circle, in which a student is said to have withdrawn over the status of a Muslim who commits a grave sin, taking an intermediate position between believer and unbeliever, and to have been named a withdrawer for it. Modern scholarship treats that origin story with caution, since it is preserved by later writers with an interest in the outcome. What is not in doubt is that Basra produced the school, with its insistence on divine unity and justice, its denial that the attributes of God are separate things, its argument that the Quran is created rather than eternal, and its confidence that reason can establish moral truth.