If a parent gets a child a pet the parent is partially responsible for the animal. Agree or disagree?

My take on it is that even if the child wanted this animal that the parent is still partially responsible. I think that they need to learn valuable things like feeding and taking care of it, but the parent should be making sure that the pet is being taken care of properly. So, yes the parent I would say has partial ownership/responsibility for this pet especially since they ultimately decided to get the animal.

My reason for writing this is because my MIL and FIL are trying to say that the cat they had for 15 years is not “theirs,” but rather their daughters and since when she moved out and didn’t take him that he is considered “mine” now. Which is a huge pain because when my MIL cleans out the litter box (because I am pregnant) she complains about it the whole time. Also, he meows and bangs on the door multiple times a night and wakes me up and this is going to be hard to deal with when I have a newborn. We told them that when we move out we are NOT taking him, but they insist that he is “my” cat. Anyways, do you agree or disagree that the parent has a liability to take care of the pet even if the child moves out years later?

Please agree to disagree.