A coach should never call out one of his players in front of the fans or opposing team. There is no excuse for it I don't care how many signs he has missed, bad base running mistakes, bad pitches swung at, errors, lack of hustle, etc. Its not a matter of a kid being able to handle it or not. Its not a matter of a kid being tough enough to shake it off. Its a matter of respecting your players and your team. You have a powerful tool as a coach. Its called the line up card. And another powerful tool. Its called the ability to remove a player from the game.
When a coach calls a player out in front of the fans and opposing team he hurts the team. He brings a negative vibe to the team. He has not addressed the problem he has simply embarrassed the player. He is trying to let everyone know that he didn't have anything to do with it and that he is upset with the player. The players team mates will not respect the coach more for this. No the complete opposite.
Pull the player to the side and say "We have talked about you missing signs and its hurting the team. I am pulling you for the rest of the game until we get this worked out." The team mates see the consequences. The player sees the consequences. They respect the way you handled it. The player respects the way you handled it. He is now focused on fixing it instead of the way you handled it.
Coaches who do this type of stuff are more concerned with the way they are looked at for having a player mess up than they are fixing the problem. If your going to preach team and were all in this together and we have to have each others back. Then you call out one of your boys like that in front of the fans and opposing team its not going to cut it. In fact its piss poor coaching. And it shows your a freaking clown. When you send that runner home and he gets hosed by 5 feet do you get called out by the players? If your going to call out your team why not?
A coach should have a bigger picture in mind. He should be more concerned with getting it fixed than acting like a child when things don't go the way planned. If a player cant get motivated by being benched to fix the issue there is no fixing it. If you think your fixing it by calling players out like this your clueless. Your creating more issues than missing signs.
How many times do you drop the F bomb on kids before it loses its shock value? If your players are missing signs there are two ways to look at it. One the player is not focused and needs to learn to get focused. Two you didn't properly coach him. Now you either fix it by dropping F bombs across the field or you sit him down and get him focused.