From a pure practical standpoint, it doesn’t make sense to eat carnivores. Terrible feed conversion. We don’t want to raise meat to feed it to meat. Traditionally, ruminants were a way of converting inedible grass into nutritious meat and dairy.
Also, carnivores are a lot harder to handle… They bite! Cats jump and dogs dig. I farm. The livestock stay inside the fence, cats and dogs go where they please.
The animals in your first list are carnivores (cats are an obligate carnivore) while the second list are herbivores or omnivores that do well on a vegetarian diet. That’s why we eat the second list and not the first.
Also humans like dogs, they’re a lot like us despite being a smelly 4-legged bitey critter. It’s quite odd, really. We’ve evolved together for millennia at this point. More so than any other species on earth, dogs have a place in our society alongside humans, with their own jobs and skill sets.