I'm not going to judge others on what they do with their bodies. It's really up to each individual as a person and as an adult to decide if they want to get a tattoo(s). However, if you wish to dissuade anyone from doing so, here are some tips.
This is probably the weakest point, but if you get a tattoo, you're basically ruining your body. It's not temporary. It's PERMANENT.
Step2
Show some pictures of old people with tattoos. On a younger person, some tattoos may look "sexy" but not when you're 80.
Step3
There's not much scientific proof (except for those tattoos done improperly) where tattoos have caused skin problems, but the potential is there. Could it cause skin cancer? Perhaps, but again, there is no real evidence to suggest it. But why take that chance?
Step4
If this is your teenager who wants to do this, it's up to you as a parent to determine if it's the right thing. Sooner or later, he/she will leave the nest and then be able to do it on their own anyway. So, be objective and let them know how you feel and how they may feel years from now after they've done it. It's hard to know how one will feel when one is 10, 20 year older. While there are procedures to remove tattoos, they will leave scars.