Is it because your tragus might grow or its not thick enough or just because you need your parents agreement at an age younger than 18?

The age of consent is 16 so I really have no idea nor do I find this age restriction on any site. Who told you it's 18?

This appears to say that anyone over 16 can consent to other than genital piercing (without parental consent) - The Law Relating to Body Piercing and Tattoos - Beauty Treatment Expert (UK) (http://www.beautytreatmentexpert.co.uk/law-relating-body-piercing-tattoos.html)

I was at selfridges - london the other day and asked if I could get a tragus piercing and was told I had to be 18 to get one.

You have to be 18 to legally get any piercings in the U.S. by yourself.