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Because she does not use Sigil. It is based on her chanting powers.

Mage followers of Archons do not use magic in same way as Archon.

It is in intuitive and raw form for Archons themselves, while for followers is more "formulaic".
 
other archons can teach their sigil to their followers (learned from ebb and the gravelight), so I really can't understand why she can't, especially when you can gain the sigil after the conquest (I really don't remember what choices you have to make for that, I bassicly did it at random, it had somehing to do with letting a mage group join the chorus but when I tried to do it again I couldn't get it)
 
It is also clear that Sirin is very different from your average Archon. Sirin was an Archon from day 1, while the others (including the fatebinder) grew into their powers (although whether they always had the potential or it could happen to anyone is a matter of debate). But perhaps more importantly than that, her headdress completely changes her powers. Despite still being an Archon, she has had her powers - and thus we can assume her ability to understand and teach those powers - restricted by it.