I'm sorry, but your mom seems to have some issues. It may be time, now that you're aged 13, to start finding ways to find value in yourself, and to ignore these types of comments from your mom. Your mom's comments aren't normal - she obviously has some issues that she needs to deal with. I don't fault her; she's human like all of us. But you need to find ways to find value in what you do, for yourself - and to not see yourself and what you do through your mom's eyes. If you need help with that, speak to a counselor at school.
With that said, it doesn't matter if others are better at this than you are. There will always be someone who is better at something than you are, or than I am. That's not the point. The point is that you enjoy what you're doing. If you no longer like skating, then you can leave it, and that's okay. But if you still like it, then keep working to progress. Maybe you land the double axel (and you probably will, if your coaches feel you will). Or maybe you won't. That doesn't mean you have to quit skating, if you like it.