Why are tattoos considered bad by the church?

One reason is completely non-religious. There is a stigmas attached to being tattooed that many older generations remember. In their days, drug-dealers, prostitutes, gang members, bikers, and other seedy figures were the only types of people who got tattoos. It is hard for older people to understand that lots of nice, respectable people are tattooed, these days.

Another reason lies in the interpretation of The Bible. One specific passage that I can cite is Leviticus 19:28, in which God warns against blood-letting and tattooing as pagan practices.

There are several different interpretations of this passage. Some say that only the "tattooing as a pagan practice" is what is wrong in God's eyes, and some say that all tattoos are wrong. However, it is really up to the individual to make that interpretation, after meditating on it and praying to God. There are people who see any kind of marking, even images of Jesus, as idolatry, because it becomes a sort of worship ritual. However, I consider myself a Christian, and know many firm Christians, with tattoos. In this day and age, tattoos are more of an adornment than anything else. While there is a spiritual element involved, I don't think the Bible is really against a little ink under your skin.