looking for a Latin root for "adult"
Only a small handful of members here know Greek, so we may not be able to offer much help.
As Bitmap said, though, the Ancients weren't too keen on political correctness - words referring to males were default, with the inclusion of females implied. Pedagogy is probably as "sexist" as andragogy, but I don't know Greek and can't say for sure.
Note that until very recently, English was like this as well - through a number of cultural movements that the Ancients never had, this changed somewhat. I believe that most Latin-based languages still use the masculine gender as default, not out of sexism but because that is simply the way their language is spoken.
There may be a gender-neutral word for "adult", but I suspect that any gender-neutral word will also be age-neutral.