Tracido: There's actually some lore as to why most animals are dead in 2077, the game is quite generous considering what's coming to the planet..
Doom3r: You have a cat living in your apartment and interacting with everything you interact there (Who puts a food into the cat's bowls?, Who adjusts the box it's living in? Who empties the box that is in the toilet? Other thing that would come out if you really live in the same space with the cat), however for whatever reason you cannot pet (in a definition of a "to stroke in a gentle or loving manner") that cat, yet you still can do that to some random cat next to the Viks Clinic. I would love to know what is the lore reason for that other than somebody (whoever was adding "Feed teh Cat" quest line) just did not thought that if you have an animal in your house it is a bit more than just a decoration or a trophy.
So true, fair questions for interaction and realistic feeling. I think the reason is the glitches. When you finally get the cat for your apartment, it glitches out and the eyes appear blind sometimes, meaning adding petting or some other behaviors and looks may have been cut.