Should you apologize when you’re RIGHT?

I recall many years ago during middle school,I was in a serious situation with a few classmates who knew they were in the wrong.One of my teachers tried to remain neutral,but I refused to apologize for having been picked on by them.Unfortunately,the situation escalated until the school principal got involved.Those classmates had convinced the principal that I had made up the whole thing in order to gain attention.Also,as a result,I was pressured to apologize even though I was in the right.I had to answer to my parents as a result.Since then,I learned to try to shy away from situations like that and others.It is unfair to be in that kind of situation.