I've had more than one person, in the youth baseball industry (travel programs), tell us as parents that them teaching our kids a curve-ball is safe as long as you teach it right, then go off and show you a cutter or slider during the demonstration or call it a "karate chop" curve. They just know if they can teach a kid to throw a pitch that does something, they'll win more games because most youth don't know how to hit it no matter how bad it is. The first time I heard that was at 11u.
The only issue as far as potential harm is probably based on the kids over manipulating the pitch for the right spin direction by forcing their arm to remain in supination through the follow through and not allow the forearm and wrist to pronate as would happen naturally after release of the ball. The old pulling down the window shade analogy gone wrong comes to mind. I'm also betting the youth arm issue is really, if a kid has a curve, he's probably considered a pitcher first, position player second, and is over used.
I prefer it not be taught for one major reason, I wouldn't want my son thinking he's "all that" throwing a looping gravity ball that kids dive out of the way of, and the umpire calls a strike cause it lands somewhere near the catchers glove. I'd rather have him learn to locate and change speeds and manipulate the fastball with finger pressure. At the youth 14 and under level I really consider a curve a trick pitch and not conducive to developing a pitcher.
I do get a little amusement from seeing a kid's face when he throws that to someone who knows how to hit it, you can just see the wheels spinning, "but, but, nobody can hit my curve"
OH, Tom House, I used to like his contributions, but I ended up blocking him from my twitter feed because of sheer volume and the click bait-ie nature of his tweets over the past year.