How do kids become mentally tough?

Mental toughness in sports can be sport specific. It can be position specific. It can be offense or defense specific. E.g., there are some pitchers who have great mental toughness on the mound. But they don't exactly exude confidence at the plate in a tight game with two outs and runners on.

It is developed, IMHO, arising from confidence/esteem (not ego).

Now this confidence/esteem can be rooted in other factors from the person's life. But it must be developed in the specific sport. Take the toughest ghetto kid in the world who is confident and a survivor. Put him in front of a good inside fastball & 99% of the time he is backing out. He hasn't developed confidence in that particular situation.

How is mental toughness developed for a pitcher in baseball?

Encouragement along the way from coaches and parents.
The coach expressing confidence in the pitcher.
Learning to deal with failure in a constructive manner.
Mental aggressiveness.
Facing tough situations and experiencing success.
Accepting the fact that he can only control his pitches, not the play of the remainder of the defense.
Judging his success by his performance, not by the performance of the remainder of the defense.
Building a foundation of confidence by remembering past successes.
Developing an attitude such that he desires to see tough situations, in order to display his strength to the world.

Just a few thoughts.