Originally Posted by horatio
Your question is as dumb as asking something like "How did TUC show that Kirk overcame his hatred for Klingons?". An appropriate answer is: "Watch the movie, it's all in there.".
I did and it wasn't. It's there in a eus ex machina sense in that they didn't like each other and the beginning and they did (sort of) at the end. But there wasn't really much to show why there was that change.
Kirk challenges Spock throughout the movie and Kirk is right one most of the challenges, but that's not really something on which a friendship is based.
If it's really in the movie, it should be easy enough to point out . . .