Cats may well live with us, but they don't live like us. I've noticed over the years that how we perceive stuff and how cats process the same info is often so different as to be almost alien. Here are a few I've been thinking about recently (all contributions of more examples gratefully received! ):
door: something a cat absolutely MUST be on the other side of, no matter what! Important exception: when the door is being held open for him by a human.
sarcasm: give a cat a small morsel of whatever you're eating, and it will spend the next 20 minutes to half an hour carefully and methodically grooming and washing itself from head to toe, as though it's just spent several hours polishing off a 9 course banquet.
sunlight: cat Kryptonite! A cat can't walk through a patch of sunlight on the floor without going all weak, and eventually collapsing in a heap.