You cut yourself when your family criticizes you. You may feel as though they are criticizing you as a person, rather than just your behavior. In your view, when your family criticizes you, they are in essence saying that you’re a bad person or that they don’t love you. That, in all likelihood, is not the message your family is attempting to convey.
I would encourage you to speak to your family about how you feel. My sense of the situation is that you are misinterpreting what they are saying. Discussing the matter can help to clarify the situation. I understand that it may be difficult to discuss such sensitive matters but it still needs to be done. It is healthy to discuss your feelings, especially those that are causing you significant distress.
Cutting is always a sign that someone is suffering and that help is required. When speaking with your family, you should also inquire about the possibility of seeing a therapist. A therapist could greatly assist you in learning more effective problem solving skills. Please take care.