She has told you that she thinks it's important to spend this holiday with family. She spends it with hers, and according to what you wrote, you spend it with yours. You're both "covered", according to her stated principle, and it's balanced.
From her perspective, you're suggesting that she give up spending time with her extended family, which is important to her, when you are not giving up time with your family, which she thinks should be important. She likely sees your request as moving the needle from "neutral" to your preference and away from hers. Especially since her family is gathering from (apparently) diverse locations; this isn't just going to the parents' house.
Being in a relationship means that sometimes the needle will be moved toward the other person, and sometimes not. So the fact that your request moves the needle isn't the problem by itself. The problem is that you apparently haven't provided offsetting motivation or taken into account the special circumstances (that larger gathering). In fact, you've told us (and maybe told her?) that you don't think it's important, and yet -- from her perspective -- you want to disrupt her family's holiday. If, on the other hand, you were suggesting that the two of you spend the holiday together (with neither family), or if you proposed hosting both families, that would be neutral in a way that "skip one family, go to the other" isn't.
If you want to persuade her, you need to take all this into account and show her that you're thinking about both of your needs, not just your own. Maybe having her join you with your family is important to you (or your family) as a way of integrating her into your clan; if so, that would be important to say. (You should, of course, then be receptive if that's why she wants you to join her on family visits.) Or maybe this holiday in particular is important to you for some reason that you will explain, but you'd be happy to join her and her family for some other major holiday that seems to matter to her. (It has to actually matter to her; don't try to make up a new tradition that her family doesn't value.)
Given that her family seems to have a big gathering planned already, you will probably have more long-term harmony if you don't try to change this one but instead talk with her about how to balance your conflicting holiday desires in the future.