I wouldn't lean on the Constitution too hard on this one. We spend an enormous amount of time, energy, and money on trying to get it accepted that it means "adults" can bear arms.
Further, the authors of the Consitution lived in a time when reaching the age of majority was a big deal. Until the age of majority, you had damn few rights and were essentially your father's "property." There're age limits on all kinds of things in this country, and there always have been. Right now, you're all fired up about it because you are on the wrong side of an age limit for something you desperately want to do. If we go to a ricer forum, I bet we can find a bunch of kids 12-15 whining that they, personally, are more than mature enough to drive and it is so unfair that a learner's permit has an age limit of 16.
On the military thing, anybody who has actually been in the military will tell you that they, if anything, make it more difficult to do gun stuff_outside of EXACTLY what and when they want_than for a civilian 18 year old. When you sign up, they don't hand you an M-4 and a crate of ammo.