This guy just can't seem to merge in with Kondou and the others because of the different way they see things. He had a lot of followers in Shinsengumi, for he was a scholar-type fellow and was able to explain his beliefs (tending to Sonno-joi) to the others and even persuade them to support his views. Finally things got to a head, Itou and his followers, including Saitou, packed up and resigned from the Shinsengumi. He was quite popular among some of the Shinsengumi members, which was why as many as 15 people packed up and went with him. Yamanami's death sentence played a part as well - see section on Yamanami on this.
But wait! Saitou's departure with him was actually Hijikata's trap, where Saitou was sent as a spy! By and by Saitou gained Itou's trust while relaying messages back to Hijikata, until finally Saitou assassinated the former advisor, and rejoined the Shinsengumi... Saitou was really a very important personnel in the Shinsengumi, ne?