It's difficult for me to understand that how difficult it is to get rid of your cat, becuase I don't own any pet. However, I can see my friends who have pets are really attached to them.
You sound very loving and caring person. Good for you.
Just keep in your mind that human life is more precious than animals. We are master of all animals. So, you can't really compare your cat with your girlfriend in term of choosing....Probably, you should tell your girlfriend that there is no comparison here...same as you can't compare apple to a chair!!! can you? so, try to talk to her that the poor cat won't have any place to live and tell her that you will try to find a way....and comfront her that she is being loved by you....and you just feel pitty for a cat now!!!
My boyfriend has a cat, a female cat. and honesty, I don't like living with animal. It's a cute cat, but she's bugging me the whole night when I'm there sleeping over....Thursday night, I couldn't sleep the whole night, becuase she was jumping on us and honesty I was thinking how unthoughtful my boyfriend is not kicking the cat out....but thank god, he did finally, he closed the door...when at 5:30am...and then I could sleep....yes, I can see the cat as a problem in future if I want to move with him...I love dog, but I'm not into cats....I don't find them friendly at all...however, I won't bother myself thinking about it now....as it comes the time, I will deal with it....and the cat is so cute....but I don't see the cat giving any kind of affection...my ex boyfriend has a dog and I really miss the dog yet...although, I didn't want the dog to sleep in our bed!!!
I know most likely you talked to your girlfriend already, but try it again....and I hope this time it works....
also, you can get a small place for the cat and put her there while your girlfriend is around....animals don't have the same feellings as us....they are just animal...your love life is more important than your pet....
good luck
Marjan