On another thread Angel HI mentioned how "AT, is one of the 3 greatest dances to learn because in its most basic sense, it is solely based on natural walking." I asked what the other two were, and the reply was Bolero and International Slow Foxtrot.
This thread is started inorder not to completely hi-jack the other thread.
So the question now is ... what are the reasons for the other two?
And perhaps the secondary questions could be ... what would others feel are the "3 greatest dances to learn" and why?
AT is, more than all other dances, based solely on the natural movement of balancing over one step at a time, and moving through the legs to the next place. Because of the nature of the movement, the options for what the next movement is and where the place is are greater than many other dances. Further, because of the "embrace" (a more natural form of "frame"), the intricacies of the lead/follow are invaluable as a learning tool for other dances.
The American tango, when danced well (not marchy as seems to be a precedent), resembles the AT much in terms of movement and footwork. Learning to dance in the middle, as opposed to from foot to foot as in other dances, increases one's awareness insurmountably for this and other dance movement skills.
Bolero (American) is a beautiful dance. I am extremely unhappy that the Bolero, since the intervention of DS, has taken on a different appeal, or trend, and lost much of its soft infinity. This was its greatest contribution to dance. Learning this dance, in its former form of glide/rise, whisk, and slight body roll on the lead's left, is paramount to becoming the best that one can be. The benefits here are: impressive contra-body movement, glide, sustained rise, impeccable balance (whisk), controlled lowers, and infinitive movement.
SF, Slow Fox has been discussed above by Chris. This is the dance that all serious BR dancers want to master. This is the highest peak. The most important things to learn in this dance...rise/lower, CBM/P, in-line and outside partner positioning. Also, how to sustain movement over a series of underlying beats. To learn how to execute and control the soft, almost slow motion, smooth, elegant movement of this dance, together with the infinitive rhythm movement of Bolero, and the mid-weighted movement of tango, will teach dancers everything they need to know in order to be a top dancers.