While the claim that tradition forbids those with tattoos from being buried in a Jewish cemetery is without merit, it is indeed true that Leviticus, and rabbinic law, strictly prohibit tattooing. According to Moses Maimonides, the proscription is a response to the pagan practice of inscribing the names of deities on one’s flesh. Menachem Levine suggests some additional explanations:
Historically, slave-owners tattooed their slaves to prove ownership, just as cowboys branded their cattle. Perhaps that was a reason that the depraved Nazis tattooed human beings at Auschwitz. In addition to a practical solution that enabled them to keep track of prisoners, it also served to dehumanize their victims and strip them of their unique identity. The formerly-free individual was now nothing more than a number, mere property of the Reich. As human beings we have a desire for freedom and an innate sense of our uniqueness. Tattooing the body does not reflect that ideal.
Our lives, [moreover], are given to us for a purpose, and our time is meant to be used to accomplish our unique mission. Similarly, our body is on loan from our Creator to fulfill our job with it. Self-inflicted gashes, excessive body piercings, or tattoos all bespeak a lack of respect and reverence for the body, and hence, for the body’s true Owner and Designer. Tattooing one’s body can be compared to etching a name onto someone else’s freshly poured cement. It is defacing property that does not belong to us.
The latter explanation is brought into stark relief by the situations in which contemporary halakhists have permitted tattooing. These, Levine explains, involve not just “pressing medical needs” but also cases where a tattoo can serve to “preserve human dignity,” such as “scar removal, reconstructive surgery after a mastectomy, or blemish corrections.” Thus rabbinic thought understands the body, and its appearance, not as a material shell to be transcended, but as an expression of the sanctity and majesty with which God has endowed mankind.
Read more on Algemeiner: https://www.algemeiner.com/2021/10/19/a-new-look-at-judaism-and-tattoos/