Why do people get tattoos, piercings, and other forms of body alteration? Mark Bauerline at First Things has scratched out his eloquent, and mildly elusive opinion. I have inserted a few choice paragraphs below.
“Why? Because while the body satisfies human desire, it also impedes it. Women want to be thinner and their hips won’t comply. Men want to bulk up, but it takes too much work. Young women think their breasts are too small, and their boyfriends agree. People wish that their skin were lighter or darker, their hair had more curl or less. Men feel trapped inside a woman’s body, women in a man’s.
The body, too, is a focus of judgment, whether we like it or not. It excites or repels. It lends itself to unwanted racial and sexual stereotypes.
To overcome the problems, the academic argument goes, we must displace a longstanding conception. People have idealized the human body, treated it as a temple, a purity, and that mystification must end. The body is NOT a natural thing or divine form. It has no natural or supernatural status. That’s what my friend meant when he insisted on coloring hair, writing words on forearms, inserting studs in tongues, and otherwise modifying the physique. We must de-naturalize the body, redefine it as a human construct. A tattoo helps turn this object we seem to have been given into material we may shape and revise. Yes, each one of us is stuck with the one we’ve got (at this point in time), but we can re-create it, fashioning it into an expression of the identity we prefer.
That’s the theory of body art. It spells a transition from the body as physique to the body as text. You can write yourself upon it. As a friend put it to me: A tattoo isn’t the Word made flesh, but the flesh made word. It may strike old-fashioned types as pedestrian narcissism and adolescent conformity, and sometimes it surely is. But in a deeper and more troubling way, it is canny and subversive artifice, spiced with a moralistic claim to personal liberation. A tattoo is a personal statement but also an anthropological position that accords with the prevailing transvaluations of our time. It’s a wholly successful one, too, judging from the entertainment and sports worlds, and youth culture. With the mainstreaming of tattoos, another factor in the natural order falls away, yet one more inversion of nature and culture, natural law and human desire. That’s not an outcome the rationalizers regret. It’s precisely the point.”
Source: A Theory for Tattoos | Mark Bauerlein | First Things
MattTroupe.net 
I’ve always taken it to be part of a spiritual war against the image of God in man. Though the average person getting a tattoo doesn’t do so consciously (but they are as you indicate trying to write their own persona on their person), the movement is one that does go much deeper and is propelled by spiritual forces. In it, man expresses his dissatisfaction with the work of God and attempts to show that they can do better. Man rejects the image and work of God and embraces the image and work of man — and in doing so unwittingly sides with the one who is fighting against God. The end becomes more readily discernible in the more extreme examples.