I like dogs and cats (I have a house dog now, my cat died last year).
That said, I find it rude how some people are with their pets when I visit.
I love to pet cats, play with cat toys with them...but I don't like to pick them up.
Though some cats like being picked up, especially by their owners, I've found that at least half of them hate it and would rather be petted on the head.
One of my closest friends has two cute cats. I like petting them while they're on the floor or on the sofa. A few times though, she was holding her cat while I was standing next to her, and said, "Here, hold Fluffy. He loves to be held." Before I could say anything, she hands me Fluffy, and he wants nothing but to be released, squirming, and I almost got scratched.
Another time, she was sitting next to me and put Fluffy on my lap. He dug his claws into my legs (not unfriendly, he was trying to brace himself, I think).
I find this very uncomfortable when people are overly pushy with their pets.
I finally told my friend that I don't like to pick up and hold cats, but I love to pet them.