You or your partner may lose your cool in an argument, but that never excuses name calling or foul language. Verbal abuse can range from insulting your looks, your intelligence, or your worth and it doesn't always include foul language. The main purpose of verbal abuse is to wear down your self esteem so that you're compliant and reliant on your partner—and no one else.
Verbal abuse in public is even worse - it's designed to humiliate the other person. Someone who does this often knows that they can control their partner easily - because who wants to be humiliated in public like that? No one. If you're on the receiving end of this kind of behavior, you'll do just about anything to keep it from happening, right? Your partner knows that - this gives him/her psychological leverage over you.