My $0.02, take it for what it is worth.
Kids want to get tats because it is the "In thing" to do. Besides, everyone's getting them, what is the big deal?
Well, here's the big deal. You want to go to an Academy. You want to earn a Commission. Ultimately, you want to serve your country as a LEADER. Leaders don't do something because it's "cool". Leaders don't follow the herd mentality. Leaders don't worry about "fitting in by showing your pride in something, permanently". Leaders worry about leading. THAT is the image you want the world to see, not your tat.
Ask yourself, when I finally get out and want that nice, well paid professional position, what do you think the guy / gal interviewing you is going to think about that tattoo? And please, none of those "well, it's hidden under my clothes" arguments. To me, that simply says "yeah, I'm not that comfortable showing this to the world, so I got one that I can cover it up easily." That just tells me you know it is slightly wrong, but you did it anyway.
The younger generation also likes to smoke a little weed once in a while. It's not that big a deal to society anymore. Everyone is doing it, even your friends. I mean, what's the harm, right? THAT is another test on whether you want to be a leader or a follower. And please, don't start going down that "well, one is illegal, and the other is not" path. We all know that unless you're growing your own, or carrying a hefty bag full of it, most law officials won't go out of their way to arrest you for it (unless you're involved in another illegal situation at the time, and in that case you have other thing to worry about). Thousands of folks smoke that stuff everyday, knowing their chances of getting in trouble with the law are practically nil. It's cracking under peer pressure that is the real test here, and leaders don't allow that to happen to themselves.
You want a tattoo? Wait until you've DONE something unique that you can be proud of for the rest of your life (participating in the Olympics may be an example). JOINING the military? Nothing special about that, thousands of kids get Academy appointments every year.
Tattoos have become pretty standard and standard for a lot in the military. Which to me smacks of "herd mentality" in the ranks. Pretty hard to be the leader when you're quick to run out and be a follower. Be a leader instead by your actions, not by the ink you got on your shoulder blade.