Natural selection has nothing to with that, although it is a common misconception. Natural selection is a key concept in evolution that refers to biological traits either becoming more or less common in an organism based on their functionality.
Like the first creature to develop primitive lungs, for example.
Plus, I am pretty sure hunting stopped being a challenge when we invented the snipe rifle, so i'm not really we need to determine if we are dominant or not over a tiny cat.
What you are thinking of is called "survival of the fittest".