It might be easier to explain why professionals don't wear vests...
In the olden days, boxing was just as corrupt then as it is today - Probably more so back then even... The idea of boxers not wearing shirts was for a very simple reason... So his opponent knew that he wasn't hiding anything, or that he didn't have a knife tucked away if things got hairy...
Both boxers would face each other, knowing there was no 'skullduggery' going on beneath their vestments. As the sport evolved, it became a standard part of the sport.
Because olympic judges are half blind dumb azzes. They can't distinguish fighters without the aid of red and blue shirts.
The white stripes on the side for the judges to see?
As a form of advertising the country they represent.
In my mind, boxing is the sort of thing that should be done shirtless. Shirts just get in the way of a good fight. Why are amateur boxers required to wear shirts?