Why do people like animals that are endangered but not animals that have adapted to live with humans?

Maybe because of the length or timeframe of reproduction of such animals. For example, rats can reproduce/multiply faster than tigers, rhinoceros and seahorse? Also, it only makes sense to save endangered animals. It's in our nature to save rarities because it's logical-- most of the times, such rare things are irreplaceable. We buy things that we can't easily find or make. We save food or money when we're running out of some. The same goes with animals.

Maybe people tend to focus more on the negative aspects of those (crows, rats, pigeons) for a number of reasons. One reason could be we simply see them more often. Another could be that they carry diseases that more directly affect us. Not as many people get diseases from tigers, but they have diseases too. There are less people in direct contact with tigers, and there are less tigers overall than rats. The idea of an animal being closer to extinction also seems to make most people more appreciative of the animals "better" qualities, because they are more "special" in a way. That could help us to understand why most people like an endangered animal more than rats or crows. I hope this helps ya!

They shot my mum, they poisoned my dad and they baked me and my buddies in a pie to set before the king, but I survived! Come on the crows!

Its because the animals that live with us are not cute. Also we don't have to worry about preserving racoons.