"Ő nem nő, hanem férfi."

Translation: He is not a woman, but a man.

[JacobKrebs]

Why can you omit articles in this context?

[Fitt3]

patience my child

[david.altmayer]

Hungarian likes to omit things :(

[vvsey]

They are not omitted. They were never there! :)

[Harly5210]

Am I the only one who feels like they should accept the singular they as a translation in sentences like these which are hard to translate without gender?

[vvsey]

What do you mean by "singular they"? Oh, you mean in the Engish translation? I'm not sure that's a good idea. I'm afraid it would cause too much confusion. Other courses just consistently accept the sentence with all possible genders.
But that's just my opinion. But this particular sentence seems too secific to be translated with "they" anyway. If I am not mistaken, "they" is used with general statements like "if somebody wants to go, they/she/he need to.....". That is not the case here, this sentence is about a specific person. Maybe "that person" instead of "they"?

[david.altmayer]

Yeah, at first I thought it could be a good idea, but I agree it could cause confusion. I'd almost rather use "it".

In this sentence though, the context makes clear that it should be "he". Otherwise, I think that either "he" or "she" is best. I guess there's no harm in accepting it as a translation, but it wouldn't be my first choice.

[vvsey]

Yes, "it" or maybe "that". But keep in mind, "ő" may be neutral, but it refers to a person, not objects. (Not necessarily a human, but it "personalizes" the subject.) So, it is like "He" or "She", minus the gender.
Yes, this one is a tricky sentence to translate to English. It just doesn't make too much sense this way. I could even imagine it with "she", with the quotation marks included:

I met my son's math teacher

How is she?

Well, "she" is not a woman, but a man.

But it could also be said like this:

It is not a "she" but a "he".

[NISHADTAKS]

How about :
'that gender neutral subject' is not a woman, but a man.
;-)