That isn't a question I would ever ask - it's too self-evident to me, down much deeper than the level where you have words. But a skeptical colleague asked me it the other day, before elaborating with the usual non-cat owner's line about how they don't really care about you, it's just about food, etc. (Though why shouldn't the food matter?)
I said it's not just that, the interaction is much more intense than that, reflecting that they have put us in the mother slot in their mental toolkits, but found it hard to explain more.
A minute after the conversation was over I thought of the additional answer that I would have liked to give. Just one among many, but at least it's a start at capturing the aesthetic angle. What's so great about cats? "They allow us to admire them as they deserve."