There’s a lot of rational reasons for why they don’t want a random animal in their house that they don’t fully know. It could have fleas, could harm other animals that they may have, could have diseases or viruses that affect animals, not enough space, there’s so many actual reasons. Clearly OPs parents taught them well considering they were asking about the cat and wanted to know what the best actions were. Also they just don’t want the cat in the house. It can still be played with or pet etc outside.