I had a woman call me a couple of years ago, while I was still doing my mobile small animal practice. She was quite distressed and asked that I come over as soon as possible and "put her dog to sleep". I asked why and she said "because its too fat!" I declined which pissed her off so I ever so politely hung up on her.
I don't believe in convenience euthanasia. If you take on the responsibility of an animal, they are not disposable because you are moving to Delaware, into a smaller apartment, or your girlfriend doesn't like dogs. Often, people who want their animals euthanized for spurious reasons refuse, when I suggest, to take their animals to the humane society for possible adoption. I've had people say, "well, I don't want him to suffer there all alone" or my personal favorite "I wouldn't want another family to be stuck with this animal's problems". Huh? I suspect that they are afraid to take their animal to the humane society because they would feel judged by a lot of people instead of just one vet trying to pay his bills.
At my first job, my boss performed (and probably still performs) convenience euthanasia. He called me into the exam room one day, a robust-looking miniature schnauzer on the table, and handed me the syringe of euthanasia solution. I asked him what was wrong with the dog and he said he didn't know but that the owner wanted it euthanized. I said no, I couldn't do it and would call the owner. The owner said she'd recently changed her job schedule and the dog was urinating and defacating in the house. There were no health problems in this five year old dog and my boss was willing to kill it because, as he put it "if I don't do it, the guy down the road will get the money ($20 at the time). The man sold his ethics cheap. The owner refused to take it to the humane society because: "I wouldn't want another family to be stuck with this animal's problems". That was the first time I heard that "reason". But sadly, not the last time.
My boss allowed the dog to be kept and cared for at the clinic for a week while I and my wife at the time found a home for it. The day aftter it was adopted out, my boss called me into the conference room where all the staff were arrayed, solemnly, like the supreme court. My boss said "We all want to know your position on euthanasia because you upset our staff with your actions". I said that I would perform euthanasia on a suffering animal that had no hope of recovery. There was a silence and he told me that they were wondering because a client was bringing in two of his four cats tomorrow to be euthanized because he was moving into a smaller apartment. I told them I'd call the client and talk with him. The client said he couldn't take the two cats to the humane society "because he didn't want them to suffer there all alone". I said at least they would have a chance of a life, wouldn't they? He agreed, but later in the day I was told he had canceled his appointment for the next day. Did he take them to the humane society or did he take them to the "guy down the road". I'll never know. But I couldn't sleep at night if I were to do convenience euthanasia. Unfortunately, there are vets in this town and this area who sleep just fine, so long as the money is coming in. It is a shame and a blight on our profession that this is happening.