The fact every single person here has stepped beyond the borders of normal TF2 to play it competitively. Games like CS, Quake and DotA are all played in the competitive format, where as 6v6 is constricting yourself in several ways. It takes a decent amount of effort to get into 6v6, and since it's not exactly what Valve had in mind, the majority of whats going on her is community driven. There's no 'the big one' tournaments held by Valve, like for instance Blizzard does at Blizzcon.

Also the fact it's entirely skill based but also made incredibly tactical by having an uber/kritz. Without it it'd just be a deathmatch fest. If you're out of grenades in CS, it barely matters if you're good at shooting stuff.

I think the CS remark there is a bit extreme (gamesense>utility>aim), but yes, utility is important.

The big plus I find that makes the game attractive is the classes system, you feel that you are playing a pivotal role in the whole 'machine' so to speak. I do have to say that I really truly hope that with the introduction of MM somewhere soon Valve Time (TM), the focus will shift more towards the competitive aspect. I think the TF2 crew has also noticed that the competitive aspect could play a big role and that showing off your e-peen (skins) is a big money machine. So best case scenario is an optimized (close to current league style) MM system which will attract new players and at the same time make them see what each class is capable of and how complex yet fun comp TF2 can be.

The whole teamplay aspect and how unique the gameplay is. As Sitebomb said

and this is very easy to notice from the first time you try comp
you notice how everyone behaves different. how the team acts as one (or tries to for that matter)

Tbh when I started all I wanted was being able to rocket jump, pull off airshots and mimicking all those epic moments on TF2 fragmovies :)
Also, we take it for granted by now, but the service that pages like TF2Lobby and now TF2Center offer for the community is amazing, specially when it comes to introducing new players to the competitive format.

It's so hard to pick a favorite aspect of competitive TF2, when there are so many good aspects that I love. I think overall in the end, the best aspect to me and my most favorite is the community.

The community is what makes a game thrive and keeps it moving forward, but not only that the comp TF2 community has amazing people in general. We have pro players that interact much more with the community, the people who create/host TF2 related sites that we use(thanks Enigma and others), the casters who dedicate their time to it, the people who are a part of the production, the people who year to year keep donating to make events happens, the charity events that we have, and so much more.

I also generally love how this community is much more personal, since we generally use Mumble to communicate, there have been people we usually hang around with in mumble and interact with much more than just playing TF2 matches, they become our friends, and overtime we make more friends through this personal interaction. If you were to go to someone's steam profile from the community, you'd probably have multiple friends in common with them. The community is small of course, but also still friendly in a way and easily interactive. Also compared to other game community forums, I always enjoyed comp TF2's the most, I genuinely enjoy how much more we're able to express ourselves in comparison to other forums we're I feel that it's much more different and we have to abide to certain standards.

The relentless, caring, and most of all amazing spirit that this community possesses is truly remarkable, to last like this over the years. Besides the community aspect, competitive TF2 also has so much to it that makes the game skillful, unique, and fun with teamplay elements. In my opinion, it's the perfect game, and if not then at least close.