In the US at least, refusing to shake hands when someone extends there's to you is quite insulting. It is fine to say I'm sorry, I'm sick, my hand is dirty, I have a medical condition that prevents me doing so, but otherwise, you are pretty much obliged to do so.
Once you've gone to their house and accepted their hospitality, you can't then say I'm still so angry at you, even if with good reason, that I won't shake your hand. A refusal, particularly one as blatant as the one described here carries with it a major social slight. In this case, since the slight was intended it is that much worse.