Personally I would be upset if I had a rescue dog and was unable to keep it - however returning a rescue dog back to the rescue centre would be the kindest thing if I did not feel I could cope with it anymore. Perhaps then it could have the chance of a life with someone who could cope with it.
I'm sure the rescue centre would not put down a dog that could be rehomed.
I'm not sure what the circumstances are but out of interest my own daughter was bitten by my fathers dog as the age of two and the dog had to be put down - and although it was my daughter it bit, I cried and cried - I couldn't have been more upset. However, I knew this was the best option all round.
Sometimes the best decisions are the hardest to make.