In general tattoos are more socially acceptable now,than they were in the past,however face tattoos don't have the same acceptance in the business world.That little piece of artwork that you want to put on your face might really look cool and trendy to you and your close friends and family,but to the person who could potentially be signing your paycheck,not so much.
Your artist is trying to do you a solid favor by getting you give this some truly serious thought before you permanently place yourself at a potential disadvantage in both your personal and professional future.
My personal thoughts on face tattoos is that they are a bad idea in general,unless you are independently wealthy,or blessed with never having to work.You should probably thank your tattooists for thinking about your future.
Seriously,think long and hard about it before you do it.