Dogs and cats and their respective owners
When you see a cat, you can pet it. It might be timid, or possibly even hostile, but the owner won't mind the least bit if you try to pet their cat, or even pick it up (so long as the cat doesn't mind). Cat owners tend to be sane, or at least not insane in the way dog owners sometimes are.
On the other hand, many dog owners apparently object strenuously to people petting their dogs without asking. They'll even claim it's like going up to a strangers' child and hugging him/her.
If this is a seeing eye dog, this makes sense. (Not the child analogy, but the 'no touchy!' rule.) Otherwise, however, these people are insane.
I'm sure there are nutty cat ladies who are the same way about their cats, but I don't think I've ever met one.