You bring up a good point in your first statement. In school we learn the rules of numbers, science, history, and maybe even a foreign language. In reality, this isn't used by everyone in everyday life. Probably the best thing learned from school (i'm talking grammar and high school) is how to behave socially...and this isn't really taught be curriculum so much as interaction with peers and teachers. Emotional training is something that would be used everyday for the rest of your life but is never taught formally (at school). How to react to difficult situations, have control over yourself, things of this nature are huge benefits of martial training. Without doing something difficult, one can never truly grow as a person. One needs a focus in their life (ie, the whole fish in the tank with a stone story). Having control of the body is the first step in controlling the rest of the self (at least one way to go about it). I think this type of training would result in less people becoming bullies, and less people succumbing to bullies.
About your "insult matches:" in my subculture in the US military these types of things go on all the time. It is a particular derivative of my specific job which includes training one to have a high level emotional control (making it a mark of professionalism to both, not succumb to verbal abuse, as well as come back with witty(er) remark of your own). For us, though, its done on such a continuous and common level that no one takes it seriously (most of the time). For those who are verbally abused at school, they are possibly somewhat sheltered and/or not very social. That being the case, verbal abuse is a unique and scary (b/c its uncomfortable) situation that they may have not developed coping mechanisms for.