I'm going to tell my girlfriend to put her cat down
Why would you make her do that?
My roommates are allergic to cats. My house has so many things that can be in danger with that cat, my HD projector, my electronic devices, my beautiful dog... Don't get me wrong, I've loved my girlfriend dearly, but that is before she brought home that cat.
I understand that you don't want a particular type of pet to live in your house, but I don't think that putting the cat down is the solution in your issue. I think it's immoral and illogical to kill a cat just because you found it as a nuisance. why not just try to make someone adopt it instead of killing it?
I don't agree with what you are saying. This is really between me and my girlfriend.
I'm voicing my opinion since you shared your problem with me. You need to talk with your girlfriend regardless, but asking your girlfriend to put down her cat is just wrong.