I've held my cats while they were being put to sleep which was very upsetting, but I felt it was the right thing to do for them.
Once when my sons were young they nagged me for a hamster. I made them wait a while until I was sure they were serious about looking after it.
To start with I asked them to sit on the floor to handle it as I was worried they might drop it. One son had a turn and then passed it to his brother to put back in the cage. Unfortunately the hamster crawled out of his hands onto the floor just as the other son stood up, lost his balance and stepped backwards.
That was the end of the new hamster. The boys were heartbroken, each blamed himself, one for being clumsy and the other for letting it go.
I didn't know whether to laugh or cry. The boys still remember that as the worst day of their lives.