What's the alternative that you want? Because for someone to give up a pet, it likely means that something big has happened, and this is the last ditch effort.
We adopted a cat from a friend (really, a boss). We were her 4th home. She was the sweetest little thing, but she seemed to have a "kick me" sign on her somewhere that only other animals could see. Her second owner's husband died and the woman made the decision to give up the cat b/c her other cats were trying to harm her. Her son found out and drove across the state, just to rescue her. He and his partner kept her for awhile, but after a month they realized that the other animals were trying to kill her. They had to lock her in a crate to protect her from the other animals (especially this one cat named Spike...seriously, name an animal Spike and you're just asking for trouble IMO). That was no way for her to live.
So they offered her to us. I was newly pregnant, I was not working, I was bored when I wasn't sleeping...a cat would be perfect.
And the first night we had her, I had my very first non-exercise-related asthma attack; it was scary.
But I'd already fallen in love with her, and we just couldn't give her back, so we kept her. She wanted to sleep on us...my lungs couldn't do it and we had to bar her from the room. She slowly was moved to smaller and smaller spaces, especially after DS arrived, b/c even DS could read the "kick me" sign, and I spent a good amount of time keeping her protected from him.
Then we moved to a new place thinking how wonderful the bigger space would be for her...and a week later our landlady (who had been our apartment manager) realized we had a cat and said she had to be kept in the garage or we had to break our lease.
While we figured out what to do, we did keep her in the garage, making it as cozy for her as possible...
During all of this time, she developed behavioural problems, she developed licking problems, she had a horrid sore on her leg that lasted a YEAR despite our having veterinary care for her...it just kept going and going b/c she would lick it (I later realized that the behaviour can go along with vaccines, which she had had shortly before it appeared)...it finally took a holistic vet who did a double whammy of a special natural wash AND a big shot of antibiotics (the antibiotics took it halfway, the wash finished it off over time).
When I clipped her nails I had asthma attacks. She stopped pooping all the way and would walk around with stuff hanging off of her. She started peeing in wrong places.
And we kept her, despite being absolutely at our wits' end, because the alternatives sounded so bad and we didn't want to be the people that dumped their pet of 3 years. She had food allergies (allergic to poultry, it turned out) and we were about to change to a raw food diet for her, she could NOT be around other pets, she shouldn't be around young children, she probably shouldn't have more vaccines given her reaction, etc etc etc...m friend kept urging me to give her up, but SHE wasn't offering to take her, and I couldn't find anyone who would do for her what needed to be done....
Sadly, she chose for us. We had MIL and FIL watching our house and feeding her while we went to my brother's, then FIL fell ill and hubby was called back home. He was at the house and found that the cat had been belly sick all over her area (still in the garage), and while he cleaned it up and fielded calls from his mom, she ran away.
It was sad. I still mourn her, and it's been as long since she went away as we had her in our lives. If we could have brought ourselves to be the people who gave up the pet, I would have been more healthy, and she might be alive today.
Of course not every case is like ours or feralpeg's. I'm sure there are cold-hearted people out there. But I just think it's wrong to assume that everyone giving up a pet is doing so coldly and as their first choice...