It doesn't have to be Binary. Regardless of how you want to argue it the game refers to Asari as having one gender, and that being Female. It doesn't mean the same as for other races because they can still reproduce. The official codex for the Asari refers to them as an all female race. If you can't wrap your head around that being a thing it is fine. But don't try to argue anything different when the game lore clearly states it as such.
http://masseffect.wikia.com/wiki/Cod...il_Races#Asari
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Goddess, Matriach, Madien, huntress, daughters, She, Her, etc. The Asari themselves use feminine titles and pronouns. They identify as females. The Asari don't label themselves as females just because they give birth. They were even created by Bioware to fill the "Green alien girls" trope made popular by Star Trek. They are female no ifs, ands, or buts.
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He may be involved but the presence of his daughter is not proof of that. Remember Cerberus is about Humans over everyone else. Cora on the other hand has trained and worked with Asari commandos and is not the typical Cerberus propaganda. What is more likely is that Cerberus pulled strings to get Cora out of the system because of the Reapers.