Your argument is centered around the assumption that it liking someone's personality is comparable to liking their looks, and then you are moving on to the assumption that many people are drawn to people who physically look like themselves.

I have never in my life seen any hint at all that either of those assumptions might be correct and as such it seems as though you trying so hard to "gain insight" that you are starting to lose sight of what the world actually looks like.

We don't generally like people with similar interests as ourselves because we love to see reflections of ourselves, and anyone who has ever shared an interest with another person knows this. It seems as if you have learned some fancy psychology concepts and are trying hard to make connections that don't really exist, just to find an application for the concept you just picked up (in this case the assumption that humans love ourselves so much that we want to surround ourselves with even more of ourselves).

You have observed that humans like spending time with others who share the same interests. That is correct. You are then trying to argue that we a) do this because of narcissistic reasons, b) that there is a comparable utility between hanging out with someone who you get along with and with someone who has a face that resembles yours, and c) that people frequently choose their friends based on closeness in physical appearance such as facial features. You are trying to connect these assumptions and observations through the concept if narcissism, thus making it an insightful sounding question. However, point A is very questionable and points B and C have absolutely no connection to how things actually are in the real world. For this reason I think that you are trying too hard to be deep.

Just my opinion, though. I may of course be wrong and I'd be very interested to find these people who supposedly choose to befriend people based on how similar their faces are!