A third reader writes:
I’m pretty sure real tatooing (as opposed to simple outside coloration such as with magic market) could well be considered a sin against the fifth commandment, since it’s an attack on your own body. As are the multiple piercings one sees these days. Anytime you willingly violate the body’s natural boundaries (skin) for non-life-saving reasons, you’re in trouble.
You seem to be taking a position that goes beyond what the Church does. The argument you use would prohibit even the piercing of ears, and the Church does not condemn that practice.
While some reason would seem to be needed to break the skin, the Church does not seem to envision it as being a grave reason like the need to save a life. Indeed, many surgeries are performed that involve breaking the skin but are for much lesser goals than saving a life.
I suspect that you probably meant "for therapeutic reasons," but the Church does not seems to require that criterion (it does for mutilation, but as noted above, tattoos do not impair body function and so are not mutilation). Things like ear piercing or tattooing can play cultural functions in some societies, and those can be important reasons as well.
Since the function of the skin is to protect the body, it would seem that the skin can be pierced as long as there is some good to be achieved that is proportionate to the risk of infection given the precautions that are being taken against infection in a particular cause. If a man decides that he’s going to make a statement about his devotion to the Blessed Virgin by having a tattoo of Our Lady of Guadalupe put on his arm then he may be able to arrange it so that the risk of infection is low enough to be counterbalanced by the good to be achieved by his making the statement.
If you can cite any current Magisterial documents to the contrary, though, I’d love to see them. Hope this helps!