Why are tattoos forbidden but piercings are allowed?
The reason why tattoos are forbidden is because G-d told us in Leviticus 16-28 that we should not put a tattoo into our bodies. The commentaries suggest that the reason is because the custom of the gentiles was to inscribe themselves with a tattoo that they are subjects of an idol, therefore this mitzva is in order to separate us from following the customs of the idol worshippers. Essentially this doesn’t apply to piercing, therefore it isn’t biblically forbidden. However there could be a potential issue with some types of piercing if it something that the gentiles do in order to be promiscuous. This involves a differant mitzva called “lo teilchi bchokos hagoyim” not to follow the gentile customs, when they are done to promote promiscuous behavior.