The problem is that while you are pregnant, the skin might react differently, you could get itchy, and tattoos are itchy already when they are healing.
As for health concerns (transmitted infections, bacteria, etc.), those are things you should ALWAYS consider when getting a tattoo. Is the equipment correctly sterilized?
Technically, you can get a tattoo while pregnant, but most artists will refuse and you have to take into consideration hormonal changes that might make healing uncomfortable, and pregnancy is uncomfortable already without a new tattoo.