If you don’t tell your mother, then you’re being dishonest — so that you don’t have to disappoint her or make her mad. The mature thing to do is to let your mom know that you’re aware that the two of you disagree, but you’ve decided to date this girl. This gives your mom the opportunity to see you making your own decisions, and to agree to disagree or to give you a difficult time — but most importantly, it gives her that opportunity. It’s a way of establishing an honest relationship — even when you don’t agree with each other.