It is thought that since pet cats knead their claws on us, lick us, or bring us their prey, they view us as if we are a valuable companion in their lives. Does this mean they perceive us as a big and weird looking cat?

I think the answer to this lies in another question: When we kiss our cats, talk to them, and play with them as if they are a valuable companion in our lives, do we view them as small and weird looking humans?