The pain they cause is real, and its effects are dangerous and nontrivial. But long term verbal abuse, of any kind, is worse than short term verbal abuse. If you always say the wrong thing, whether as victim or as attacker,assertiveness training will only teach you how to say the wrong thing far more effectively and articulately. That's not an improvement. Assertiveness training can be very helpful, but it's not a solution for verbal abuse.
Verbal violence is where physical violence begins.
We have to teach our children about this more carefully than we do. They learn that when their words hurt other people, something is wrong with those people. We shouldn't be surprised if that message gets transferred to physical abuse. In some ways, yes, but there are critical differences. The verbal abuser's need is to get and hold the victim's attention, along with the emotional reactions that are evidence of the power to do so.