I don't think the young catcher did anything wrong. Perhaps he can show his leadership quietly when they get back into the dugout and remind the 2b that "I've made that mistake before myself when I try and rush my throws to pick a kid off stealing 2b. I know you can make that throw with accuracy. Give yourself a chance to set yourself without rushing and make the accurate throw. I know you will make it perfectly next time." Similarly, I don't see why the coach didn't handle it the same way. He could have told your son in the dugout how he wants those things to be handled in the future.
Put yourself in the other person's shoes. Every player on the planet, including the best in the world make mistakes. Positive criticism is sometimes better delivered behind the scenes rather than in front of everyone when everyone (including the offending player) on the field and in the stands already knows there was a mistake.