According to Star Trek (2009) movie, Kirk became captain of USS Enterprise NCC-1701 when he was much younger than he was in TOS. In TOS, it was shown that Christopher Pike was captain of Enterprise 13 years prior to Kirk's 5 year mission. Why was Kirk replaced with Christopher Pike?
J. J. Abrams has confirmed 100% that the 2009 film is in an alternate timeline to TOS, so the events for Kirk and Pike can be completely different between the two.
The notion that when this one character arrived – Nero – that basically the timeline is altered at that moment. So everything forward is essentially an alternative timeline. That is not to say that everything that happened in the original series doesn’t exist. ... We are simply saying that from this moment in the opening scene of the movie, that everything people knew of Star Trek splits off into another timeline.
They're not in the same continuity. The 2009 film exists in an alternate timeline to TOS.
In the original timeline, Kirk succeeded Pike as captain of the Enterprise. Pike was promoted and later badly injured, as seen in the TOS episode "The Menagerie".
In the new alternate timeline:
Pike was still captain of the Enterprise, but events unfolded differently. Certain things happen similarly to the way they happened in the original timeline, but several years earlier and with significant differences. Pike is injured at the hands of the Romulans rather than by exposure to delta rays. We see him in a wheelchair at the end of the movie; presumably he is unfit to continue as captain, or at least unwilling to do so. Meanwhile, Kirk has demonstrated an outstanding ability to command a starship (again, several years earlier), and is given command of the Enterprise. In the original timeline, he didn't have the opportunity to demonstrate his ability this early, and Pike remained in command of the Enterprise so it wouldn't have been available anyway.
The numerous parallels between the original and alternate timelines require, IMHO, considerable suspension of disbelief. The members of the crew follow very different paths in the two timelines, but both sets of path lead to the same end, with all of them serving together on the Enterprise. Either it's a case of artistic license (which I'm willing to accept), or there's some explanation for the parallels that might be explained in future movies and/or books.
In TOS, Kirk got the Enterprise, when both he and Captain Pike got promoted. Pike got crippled in an accident aboard an unnamed starship.
In the Abrams film, Pike was captured and crippled by Nero, which led to Kirk taking command, and Kirk's official promotion.