If your mom hates the rat so much, who is paying for the neutering, and what if he bites your brother after he gets neutered?????? Did ya think about that at all??????

I'd rather take my pet to a stinky building, and have its life spared...than kill it. You wouldn't be responsible if it bit the new owner, so you can't worry about that. Is there only one Humane Society in the area?? Can't you take it to a different one??

which is why I want to get him neutered...
That might not solve the problem. Just because his testicles are missing doesn't mean he can't bite and act aggressive.