I often find myself attempting to explain to people the why behind choosing to devote a significant portion of my free time to social dance, and Argentine tango* in particular.
Social partner dance is fun on a basic, human level: it's structured interaction with a variety of people, often from a great variety of backgrounds (both cultural and professional). There's the endorphin high from the exercise. There's the joy of movement connected to music, which is a way of experiencing two different kinds of art at once. And the lead-follow interaction is a form of physical communication you don't get many other ways.
Argentine tango is more, though. They say it's the hardest of the social dances to learn, for many reasons. There is no real basic step, no pattern inherent in the movement to hold on to. You could, hypothetically, go into any move in any rhythm at any point in the dance, which makes it even more essential than most dances to listen intently to - and match - whatever the music happens to be doing at the moment. It is danced almost entirely in closed embrace, with the leader's chest communicating the movement. There is often a shared point of balance between the dancers through that chest connection, which creates that upside-down V shape so characteristic of tango, and which requires a great deal of balance and strength on the part of the dancers. True tango is entirely improvisation, and the best dancers will even perform without having choreographed it first (as opposed to, say, ballroom, where couples rehearse the same three minute routine for months on end).
In most social dances you can attain proficiency in a couple of years at most (even less for simpler dances like two-step and blues), but two steady years of tango might put you at the low end of intermediate. And it is a perpetual challenge. As soon as you think you've mastered one aspect of it, you discover how much more you don't know. That challenge proves endlessly exciting to me.
There's also a ritualism to tango that doesn't exist in other dances. There's an entire culture of behavior that goes along with the dance - the codigos. They're mostly designed to make an evening of dancing as enjoyable as possible for everyone, but they add another layer of complexity to what is already a complex dance. As I've moved through other dance communities, I find I consistently prefer the rationale behind tango culture.
For example, tango is the only dance I'm aware of that routinely uses body language to request a dance, in what is called the cabeceo: two potential partners make eye contact; typically the lead nods, the follow returns the nod, and then the lead walks over to escort the follow to the floor. (Especially here and among friends, the nod can turn into wiggling eyebrows and silly expressions, and may be initiated by either partner, but the structure remains the same.) It saves many forms of embarrassment once you get the hang of it, as if you don't want to dance with someone you should be able to simply avoid eye contact with them, thereby skipping the awkwardness of an outright refusal. A verbal request seems gauche, even in other dances, after you've adapted to the cabeceo; it comes off as unnecessarily pushy, especially when the entire point of social dance is non-verbal communication.
The general tenor of the emotion in tango also greatly appeals to me. The "passion" that gets so over-blown in tango caricatures is, in the real dance, quite varied and often powerful. Even what sound like upbeat melodies often turn out to have melancholy lyrics, and the balance of that dichotomy I find endlessly interesting.
Although videos are generally inadequate and don't capture the true visual appeal of the dance when you watch it live - and certainly don't at all approximate the feeling of dancing it yourself - ending with a couple visual examples certainly can't hurt.
The variance between her small adornos (decorations) and the energy at the end is awesome.
If any of this appeals to you, I strongly recommend taking some beginner classes in your area. Most places don't require that you bring a partner, and despite its difficulty, tango is incredibly rewarding. If you're in Tucson, we have a tango calendar of events: http://tucsontango.com/. The Phoenix calendar is here. Elsewhere, a Google search of "argentine tango" and your city should bring up results.
Also, if you haven't seen them, I have a post about learning a social dance and one on tango shoes you might enjoy.
* Note: American ballroom tango is something different, essentially a cheesy bastardization - that ridiculous stereotype of the man with the rose in his mouth - and is not at all what I'm talking about here.