Would you?
Have you ever?
Why?
I had to give away a kitten I got as a gift once. My parents wouldn't let me keep it. These days I have whatever pet I like (currently have a dog, cat, 3 of her kittens and a goldfish). I wouldn't give away any other pets (cept the kittens ... 4 cats is a bit much for a caravan), but some people have other reasons for giving up their pets. Some may not be able to afford the care or food, others move and find they can't take their pet with them. The cruelest types are when they can; t be bothered with their pet any more and 'dump' it somewhere, like on the street or at an animal shelter.
everybody has reasons for getting rid of a pet food, money, time, living situation, if it bites or not and so forth. I had to get rid of a dog for biting at my kids.