The phraseology of the question is quite interesting. I understand it to be 'reasons why I don't deserve to cause harm to myself', as opposed to 'reasons why I don't deserve to be harmed by myself'. Does that make sense? Or I could be reading too much into the wording
If it's the first, I think it's asking the self harmer why they don't deserve to do what they do. When I think about this question, I get slightly defensive thoughts, if that makes sense? For example, I don't deserve to hurt myself because I know there's better ways of dealing with my emotions, I know that there's better ways of expressing my pain and the part of myself that's being hurt, doesn't deserve it. So it's like it's asking the harmer part of me to identify reasons why what I'm doing to the other part of me is wrong. If you were to seperate the self harming part of yourself away from the other part of yourself and apply it to two people, ask yourself why you wouldn't deserve to hurt another person e.g. I don't deserve to box Sean just because things are really sh**ty for me right now. The reason being because it's not going to make things any better, I know there's other things I could do to make myself feel better and it's not fair to Sean to take it out on him.
P.S. this kind of makes sense to me, but I don't know if will make sense to anyone else...sorry