To keep our edge, when the world has lost it. An outlet for everything that you bottle up. To learn how to protect people you care about. For the sheer animal pride you feel when you stand over an opponent that you defeated with your own hands, on even terms. Many reasons, each unique to that person.
I personally train and compete because unlike anything else in the world, you really feel ALIVE when you step onto a mat or into a ring. You are faster, stronger, and more alert than at any other time in your life. Fear, and pre-fight jitters are gone. You don't care about that fight with your girl, that bad test, or this family problem, the world is between you and your opponent. When its all over and you stand over him and feel the crowd cheer, it is better than any drug, any vice in the world.
The wall of my HS wrestling room had a mural that only made sense to people on the team, people who had fought and bled for victory.
It was wrestler's hand raised in a referee's hand. The quotation read
If all of the pain
and sacrifice was worth it
Now you know"
I don't think anyone can forget that first moment.