Are friends worth keeping after they cross the line?

Whether you are talkig about a close friend or a girlfriend or boyfriend we all know that we get into arguments with them. But what if they cross the line and hurt your feelings severely. It is worth for you to fight for the friendship that you used to have or should you drop it and not give them another look back. In my opinion I think that you shouldn't fight for a friendship that you think isn't worth it hut when I express my ideas other people say you need to stick with you "friends" no matter what.