There is no greater privilege than having a cat decide that they like you. Most of them are so fickle with their affections, and it's hard to know what you did right when one decides to grace you with their presence. For better or worse, it means you're one of the chosen ones. We love nothing better than adorable moment that feeds our main character syndrome.
Another thing that's special about it is that most of us don't get the opportunity to meet a new cat that takes a shine to us very often. As a result, we have to supplement that euphoria with other things. Cat memes are an obvious antidote here, because they're great at replicating that warm fuzzy feeling. With the sheer variety they display, it's also a wonder that we ever bother getting our internet humor in any other way. They are just too darn funny.