I'm aware that technically he/him are both gender neutral, as they derive from "human"(Latin) and not "man"(German).
None the less, in today's common usage, it has lost that multifaceted meaning and the preferred language today is using the 3rd person as the gender neutral pronoun, or s/he or he/she.
While "they" may be the more common usage (though I personally doubt it), it doesn't really matter: it's fine to use whatever you want, and there's no reason to call him on it when it's not actually sexist. I have no problem with you using "they", but I don't see any reason to have a problem with the OP using "he", either.
> While "they" may be the more common usage (though I personally doubt it), it doesn't really matter
In your opinion. It matters to some people.
> it's fine to use whatever you want
Be aware that if you use the "he" form with some audiences, you will get a negative reaction. As to whether this is "fine" it depends on the purpose of your communication.
And even if it was derived from that word, words change mening over time so the current meaning could be radically different from the ancient meaning. For example, "silly": http://www.etymonline.com/index.php?term=silly
> the preferred language today is using the 3rd person as the gender neutral pronoun
"he", "she", "it" and "they" are all 3rd person pronouns. I'm guessing you meant the 3rd person plural pronoun ("they").
None the less, in today's common usage, it has lost that multifaceted meaning and the preferred language today is using the 3rd person as the gender neutral pronoun, or s/he or he/she.