I'd say the best thing about fencing is the seeming simplicity and purity that one encounters while on the piste. I'm not talking about simplicity and purity with respect to your opponents but the purity and simplicity that (for me at least) that you get when you're confronted with some person who wants to stab/slash/hack at you with a weapon.
The focus that you get when on the piste is quite amazing -- all the cares of the world fall off as you focus wholeheartedly on :
a) not getting hit
b) hitting the other person
I think it's mostly a survival thing. It beings out some of the most basic instincts that humans have -- survival and aggression in the pursuit of survival. But this instinct is tempered by the active mental processes that are required by the activity and the rules. In a way it's artificial survival -- survival based on the rules of the game. It's a game that has its roots in duelling and I think the sport version has successfully been able to translate (as much as possible anyway) the rush, the excitement, and, perhaps artificially, the danger of duelling. In a real duel, you KNOW you can get killed and/or severely wounded (witness some of those pictures of aftermaths of duels -- lopped off heads, limbs, bleeding torsos, etc.). In fencing you CAN'T get that type of injury but the instruments and the skills being used and developed are a direct descendant of the instruments and skills used for duelling. (With a lot of safety thrown in, of course)
I don't think any other type of sport can provide this type of focus. By this I mean that combat sports can provide that focus. Running, bicycling, etc., can provide focus but that focus is not, by any means, visceral and as deep seated as what one gets with a combat sport. I think with a combat sport, even though you know it's "safe", you can't help but feel that "fight or flight" instinct. And with fencing it's doubly bad since your opponent has a weapon and does not have a human face (the mask is on).
I guess the mask makes it easier as well to hit your opponent. With the mask on, the opponent becomes anonymous, merely some faceless entity that is trying to stab/slash you. If you could see through the mask or if there was no mask, the humanity of your opponent is revealed and I'm sure there are some out there who may have issues with striking an entity who they can ALWAYS see as being human. But with the mask on, that opponent is this faceless thing in white with a weapon in its hand. This makes it easier for you to hit them.
So, with fencing you feel "justified" in hitting your opponent. It doesn't look human (no human face) and it is trying to hit you back. This makes it easier to focus -- your humanity can be subsumed in the instinctive/logical moves that you develop over time as you progress in your fencing.
As I said, that focus is pure -- hit or be hit. Nothing more, nothing less. At least it's no longer kill or be killed.
I guess one can call it the purity of the piste.
By the way, I'm mostly talking about epee here.
