Alex....While I admit I am not a cat whisperer, I have been Mom to many feline in my day and feel I can try to suggest a few possible reasons for your dilemma.
By the info you provide, it would seem to me, because cats are all so uniquely different from one another and of course, very independent in their basic nature, your cat may be:
1.) Simply trying to tell you she does not LIKE being picked up and isn't going to let you win.
2.) Perhaps someone (without your knowledge) recently upset or frightened her by being rough and aggressive with her?
3.) May be simply going through a stage and you need to be patient. You might try a few different approaches...........OR
4.) You probably should accept that she will give and receive affection and/or being held, when she damned well pleases and that's that.
The best thing you can do with most cats is just allow them to be who they are and let them set the ground rules for your relationship. Some cats are lovey-dovey and enjoy being held and cuddled and others want no part of it.
Good luck. Meow, Paula