iirc, the original canon reasons are that, first, he was very obviously not emotionally ready and, second, Chancellor Palpatine
ordered
it. He wanted Anakin on the Council as his proxy. They did not trust Anakin, but this is about the time they started to grow more suspicious of Palpatine's ambitions as well. They only conceded him the Council seat, because they were in the middle of a war and causing political problems with the Republic would have been undesireable. Naturally, this was a setup by Palpatine to drive a wedge between Anakin and the Jedi. He knew they wouldn't make him a Master and that it would trigger all of his insecurities, anxieties, and suspicions over his role, not being trusted, etc., along with being denied access to potential Jedi knowledge that could save Padm.
idk how much of this has been consigned to Legends now, though.