Dogs exist because for thousands of years humans, recognising individually they are incapable of giving unconditional love, and less capable of digesting it, settled for second best.
Cats have been Gods for humans much longer than Jesus has.
Your Dog is a pack animal. that sideways glance it gives you while shitting isn't some existential anal catholic residue. If you could face the opposite way and literally, watch its back, then that would be great and that's what it's checking on.
If wishing to properly introduce yourself to a cat take scent from under your arm on your fingers and present it. It saves time. Also Cats love earwax.