The *one* missing greek letter.
 

There are two greek letters which do not occur in the name of any of the NIC Fraternities and *one* of those two also does not occur in the NPC Sororities, NPHC F/S, NALFO F/S, National APIA Panhellenic Association F/S, or the PFA Professionals. The missing letter is ????

Eta?

Has to be, right?

NIC: Eta and Omicron

The rest: Eta

Correct.

I may be misreading this, but are you saying that there are no organizations in the groups listed above that have "Eta" in their name? There is Kappa Eta Kappa, a co-ed engineering fraternity.

On Wikipedia (which I admit may not be completely accurate), I see Kappa Eta Kappa listed as a former member of the PFA. Do they now fall under one of the other councils/associations?

They were a charterer of the PIC, the Professional Interfraternity Conference, but left the PIC at some point prior to the merger with the PPA to form the PFA. (And I'm responsible for most of the info on that page, so whatever you can find to add/contradict things on there I would appreciate)

Hmm, now, the question is why? OK if this true?

My expectation is that you would find guesses only, I don't know if Eta is particularly rare in starting words in Ancient Greek.