Well, mostly because it's awesome. Fascinating. Totally engaging. Unique. A great workout for body and mind. Fun.
You might enjoy reading this article, slightly adapted from a 1995 issue of American Fencing Magazine, which focuses on some of the sport's unique benefits:
Why Your Kid (or you) Should Fence
By Richard Cherry
Fencing is a skill sport. Fencers train for the physical and psychological challenges of face to face combat.
Fencing demands self-discipline. Win or lose, the fencer alone is ultimately responsible. Every athlete who stays in the sport of fencing learns to accept responsibility for his/her actions and to understand that improvement only comes with work.
Fencers learn to forge friendships with their opponents off the strip. After all, they frequently train together and see each other at tournaments.
Fencing is one of the few sports where boys and girls compete against each other on equal terms, no special concessions granted, no point-shaving given. If you’re looking for an environment that fosters gender equity, it’s on the strip.
Fencers learn to accept authority: since the action travels so quickly, the calls referees make are often subject to interpretation, and the ref has the final word. At the same time, fencers learn to respectfully question authority.
In addition, fencers learn to become authorities. As fencers regularly referee each other, they learn to make decisions with confidence, explain these decisions intelligently, and control their actions on and off the strip, often under the critical eye of their peers and an audience. Fencers learn to share. They share equipment, of course, but also knowledge, coaching each other through practice and bouts and tournaments. Fencers help each other improve: it's more fun to fence better fencers.
Fencers develop the ability to establish long-term goals. Many young fencers realize they don’t have the knowledge or the experience to beat a particular opponent or win a tournament. They learn to set personal goals for themselves, for example, at least one touch against each opponent in a meet. Fencers can, and do, learn to be winners before they ever get a medal.
Richard Cherry has served as the Junior Olympic Chair for the Oregon Division in addition to coaching young fencers.
Also... Thinking about college? Take a look at these scholarship statistics. There are 40-50 NCAA varsity programs, in addition to about 90 club teams. There are very few high school programs to feed them. Therefore, you have better odds of winning scholarships and participating in fencing at the college level than, really, in any other sport. Become a good fencer, and you become very attractive to many schools.