I disagree completely. If you feel comfortable with any item at any age and will treat it respectfully, then I think it is right for you.
However, the caveat is that you actually have to be able to lay hands on said item by honest means. If it's your mum's property and she doesn't think you should have it, there's not much you can do about it; her property, her opinion is the one that matters.
However, there's no reason you can't try to change her mind. Proving your maturity is always a good way to go, and you could always respectfully show her photos of celebs in and around your age with H bags- the Olsen twins and Heidi Montag spring to mind (although Heidi might not be the best comparison you want to draw).
Whatever you do, don't whine at her, or it will only convince her of her convictions that you aren't adult enough to be gifted with such an expensive 'status' item. ...Speaking of which, you might want to ask yourself if you really would feel comfortable with a Birkin. I'm a bit older than you (27) and I know I'm more conscious with my H-bags than Balenciagas or Chanels. Do you really want that sort of attention and responsibility?
If the answer is yes, then perhaps ask if you can borrow one of hers to take to an event you're both going to. That way, she can see that you're not careless with it, and that there isn't a collective gasp of horror when you enter the room at how ghastly and inappropriate it is for you to be carrying it.
Best of luck to both you and your mum with your bag-choosing decisions.