After Kirk was thrown out of the USS Enterprise and he met Spock Prime, Spock Prime suggested to Kirk that he should take over from Spock and become the captain of the USS Enterprise.
Well, in the original timeline, Kirk was an awesome captain, but this wasn't the original timeline. Lots of things were different. For example, in the original timeline, Kirk's father didn't get killed just after his birth. This small change can have a profound effect on one's personality. He was raised by his father. His father became his early motivation to him (mentioned in Star Trek (2009) I believe). In the new timeline, he got his motivation to join Starfleet from Christopher Pike. Up until that point, he was a complete jerk who would pick bar fights over a girl's name.
In-universe, whatever happened might have given Kirk the same or similar personality by luck, but what made a genius like Spock Prime think that Kirk would be a better captain of the USS Enterprise than young Spock? Spock was appointed captain by Starfleet and Kirk was just thrown out of the ship over a barbaric issue.