It isn't your fault. Bullying is never the right thing to do, and if someone does bully you it shows that their character is flawed.

The best way you can help them improve is to say no and cut the bond, so they feel the consequences of their actions. If you just accept it and let it fly, they will keep doing the same thing to others, hurting and pushing them away in the process. He makes his own life and the life of those around him worse until they change.

Please, don't blame yourself for their mistakes. Help both them and yourself by saying that the line has been crossed. If they take responsibility for their actions and apologizes sincerely to you without you contacting them, you can reconsider whether it is worth giving them another chance.

If you do take them back, the line has to be even harder than it was before. If they cross it again even slightly, it was just sweet talk and they didn't take the warning seriously. Getting stuck in an abusive relationship is not worth it.