You should never cut yourself honey :( He should not support you cutting yourself, he should support helping you get through whatever is causing you to do it in a healthy manner.
Be supportive of course!
he should stick to you and tell you not to hurt yourself..
If he leaves or stays, you're still putting him in the "take care of me" position and he doesn't know how to handle that for a person who cuts. And that really sucks.
Everyone reacts differently. Many people can't deal with the thought that someone is doing something like that to themselves. Guys around your age are still trying to figure out their own thoughts and feelings without having to support another person's thoughts and feelings.