If you turn your back on someone or something, it means you’re don’t care what happens to them anymore and won’t help them no matter what.

Your cat may turn its back on you, but don’t worry. We’ll be back.
A cat teaching English? Really?
If you turn your back on someone or something, it means you’re don’t care what happens to them anymore and won’t help them no matter what.
Your cat may turn its back on you, but don’t worry. We’ll be back.