One of my cats, despite being an extreme clinger, absolutely will not tolerate being picked up under any circumstance.

Lone exception? If there’s a bug she wants but can’t reach, she will meow until I come lift her up to catch it. One hand under her hind legs, one under her stomach - so she has both front paws free to pin the bug with. Fortunately, she’ll let me summon her too, so whenever there’s a moth or something hanging out on the ceiling, I yell “bug” and the cat comes running to catch it for me.

Right ol’ on-demand vacuum cleaner, that one.