Maybe due to fear (at that time) that the pets would transmit COVID to human. One example is this hamster cull at a Hong Kong pet store [1].
Most likely it was some misinformed overzealous local official. Pets from pretty early on in the pandemic have been known to catch corona. I think the question of if you can catch the virus from a pet is inconclusive (last I heard) - but obviously very unlikely
If you are trying to get to zero COVID so your city isn't shutdown and thousands of people don't loose their way of life then you're prolly quarantining sick people. No one to take care of their potentially disease spreading pets, so local official decides better safe than sorry
It's messed up, but it's totally not unreasonable for someone on the local level to make this kind of call in a high pressure situation with minimal guidelines and the safety of a city on the line
In any case, in the end it's all political posturing and propaganda from all sides but I don't think it's great to be framing things in terms of "well, this bad thing is actually not as bad as this worse thing, so we can overlook the less bad thing."