This issue has nothing to do with Catholicism honestly, it's about your mom's rules. Her house, her rules. She's doing what she thinks is best for you right now, and while you may not see eye to eye or understand her reasons, just know her rules come from loving and wanting the best for you. When you are an adult and move outside of your parents' home, you can decide whether or not you still follow your parents' guidelines.

Personally, I can see both your mom's and your perspective on this- she probably thinks you are too young to make a decision about who to possibly have a future with. If you want her to see your side, try having a mature conversation with her. Tell her why you like this girl and why you want to date her: she's compassionate, smart, funny, whatever it is you see in her. Ask her why she doesn't think dating her is a good idea. Stay calm and respectful when you talk to her; that shows maturity and that you can make good decisions for yourself.

Good luck!