Many denominations of Christianity look down on tattoos and tattooing as a practice. Some look down on it because it's a "worldly practice", other's I've talked to say they are against tattoo's because the origins are from paganism and the occult (not sure if that is accurate or not), and other's simply look down on it because it's just a cultural taboo.
But seldom do I hear Christians who are against tattooing cite actual Scriptural support for their stance.
I have three substantial tattoos, so you can already guess my position on the issue.
The only Scriptural support against tattooing is in the Old Testament: Leviticus 19:28 says the Jews were forbidden to cut themselves for the dead, or tattoo themselves.
However, I do not understand myself to be bound to this Old Testament law on account of Christ setting me free from the Jewish Law (just as Paul rebuked Peter for coercing the early Gentile believers to keep the Jewish law).
And if I were to say I should keep that particular law, then I would also be bound to the commandments that sit beside it in the same chapter to "not shave around the sides of your head, or trim your beard," (Lev 19:27) and "not sow your field with mixed seed", "nor shall a garment of mixed linen and wool come upon you." (Lev 19:19)
In fact, we even read in Acts 10 where God showed Peter a vision of all sorts of animals that He had previously told the Jews they could not eat because those animals were unclean, then He tells Peter, "Rise, kill and eat," to which Peter replies, "Not so, Lord. I've never eaten anything unclean or impure!" To which God quickly rebukes Peter saying, "Do not call anything unclean which God has made pure."
So while the whole point of this experience for Peter was to reveal to him that it was God's purpose to include Gentiles in His plan of salvation, God makes the point by commanding Peter to do something which He previously told his people not to do.
This doesn't mean we completely throw out the law and everything in it, because I certainly do agree with the commandment to "not prostitute your daughter, to cause her to be a harlot" (Lev 19:29).
Personally I think it means we are to "rightly divide the Word of Truth" by learning what God's law was meant to reveal to us about Him, and connecting that with what He revealed to us about Himself in Jesus.
So the big question is:
Does my argument hold up Scripturally that we are not bound to keep the Old Testament law forbidding tattoos, or is there some context of the Scripture which I am missing that would support keeping that Old Testament law?