Turkish Airlines Cat Booking Problem - Pet Policy Change

I will be flying with Turkish Airlines from Ankara to Zurich, with a connecting flight in Istanbul. I would like to add a cat to the second leg of my trip, which is Istanbul–Zurich. I am completely sure that I have done this several times before. However, I am now being told that it is not possible and that the cat must board the plane in Ankara instead. This option costs more, and even if I agree to it, they say the cat will not be allowed on the second leg if it doesn’t board in Ankara. I feel like they make up new rules each time to make traveling with pets more difficult.