Fine -- if your kid tells you that you don't deserve a Mother's Day or a Father's Day present from him. then tell him that, in that case, he doesn't deserve a birthday present or a Christmas present from you and not to expect any.
I would definitely ask why they felt that way, and how they would feel if you were to tell them that you thought they didn't deserve a gift. Your son might be having other issues going on , maybe issues at school or with his emotions, puberty, somethings changing with his family (parents fighting) . Could be anything going on and this is how he is showing you that something is wrong. Mainly because he most likely doesn't know any other way to express his feelings.some how you need to get together with him and sit down get coffee and remind him you LOVE HIM!! I think he needs to talk, if he won't with you then you need to find someone he can trust and talk with. Definitely get him counseling, and maybe yourself as well. It can't hurt.
I wish you the best.
Remember to tell him you love him and give him a hug!