I plan on asking my date why we should not hold hands and also ask if it has to do with her culture?
Why do you specifically plan on asking her about holding hands.
Because I want to find out for sure why she wouldn't hold hands with me
It's understandable that you feel offended by your date not wanting to hold your hand. Asking her about this will give you clarity and help her to understand how you feel about it.
I'm just going to ask her why she won't hold my hand, if I don't get a good answer I'll move on.
This sounds like a good idea. She should be able to give you a solid answer if she is being honest with you. If she is just not interested than that should be fine.