Q:

Why was DC’s Anarky a minor? 

The character was introduced in 1989, an extremist who is also a child prodigy (twelve years old in first comic). 
Despite being very young he had a lot of followers for the people he was preaching to, the homeless of Gotham. 
What bothers me is, why might the writers have portrayed him as a child (even for his mature IQ) who could understand all these concepts and was willing to persuade grown men to join him?  What was the point? 

A:

From Wikipedia:

Originally inspired by his personal political leanings, Alan Grant entertained the idea of interjecting anarchist philosophy into Batman comic books.  In an attempt to emulate the success of Chopper, a rebellious youth in Judge Dredd, he conceptualized a character as a twelve-year-old anarchist vigilante, who readers would sympathize with despite the character's harsh methods. 

This part of the article is sourced to Alan Grant's intro to an Anarky trade paperback. 
Grant, Alan (1999). " Intro by Alan Grant".  Batman: Anarky.  New York: DC Comics.  pp.  3–4.  ISBN 1-56389-437-8. 
So it appears the character's youth was meant to emulate that of a Judge Dredd character. ( It's interesting, too, that Chopper, per the Wikipedia entry for that character, was created for 2000AD by writer John Wagner, who was a frequent co-writer with Alan Grant on a lot of stuff.)