Um, have you ever had a pet rat? I have had quite a few actually, before I ever got into snakes. Rats are smart & trainable (comparable to dogs & cats!)
& even affectionate at times. I can't speak for rabbits, as I've never kept them, but I like & have raised many hamsters too (Russian dwarf, that is...they
are social, while the Syrian hamsters are not). Hamsters don't have quite the smarts that rats do, they're just "cuter". But don't make assumptions, ok???
This discussion was started on cats because of the overwhelming numbers that shelters can no longer manage, as the OP explained. Similar situation for
dogs, sadly & to our disgrace as a nation of "animal lovers". This is NOT an attempt to "throw the kitten in..." despite the thread title.