Taking off your shirt might be used as a scare tactic to intimidate the person you are about to fight, or it could simply be used to pump you up, and plus by taking your shirt off it keeps someone from grabbing it and ripping it or pulling it over your head lol
So your opponent does not have anything to grab hold of to control you. Better movement. Intimidation and so your shirt does not get torn or dirty.
So his dad/mommy won't smack him around when he/she sees his shirt has grass stains or blood on it/is ruined.and that he was in a fight..
So they can show off the location of their liver and kidneys to people who actually know how to fight for real.
They must like to show this as a sign of manliness and big themself in front of the ladies
It makes them look tougher and more intimidating. If one has a six-pack, it's harder for the other to beat him maybe? A very thin guy would be more reluctant taking his shirt off unless he has a big ego ;)