I am not sure about the grammatical rules but I think you cannot miss the verb in every situation for example Én nő vagyok (I am a woman) , Te nő vagy (You are a woman). Nők vagyunk (We are women) Nők vagytok (You are women) But! I don't know why you may omit the verb in with or without an article Ő (egy) nő (She is a woman) in plural Ők nők (They are women.)
Nem jó a fordítás! He is a man = Ő egy férfi | És nem pedig "Ő férfi"!
Often the verb is not necessary to get the message across -- especially in sentences that involve linking verbs.
The verb -- van (to be) -- plays a role as a linking verb and férfi is the compliment. In such sentences it is common place, perhaps mandatory in some instances (I'm not completely sure about that), to drop the linking verb in such simple sentences where a pronoun and its compliment are enough to get the message across.
Recall in Dutch, "Ik ben student" (I am a student) -- the article (a) is not necessary, as zijn forms the link between the subject (Ik) and the compliment (student).
The much more elaborate dropping of sentence components (compared to Dutch, for example) is just one of the many cool features of Hungarian ^_^
Here the 3rd person singular pronoun denotes the grammatical number (e.g. I, you, he/she/it, etc.). As you may have already noticed (otherwise you'll eventually learn that) there are two sets of conjugations for verbs: Definite and Indefinite -- each conjugation for each grammatical number is different and, thus, the pronoun can often be dropped. Indeed in most cases the leading pronoun should be dropped unless emphasis is intended to be placed on the subject.
This example is just the opposite: No verb, thus, a pronoun is needed to indicate grammatical number. Because Hungarian has no grammatical gender, the compliment itself provides enough context as to whether ő means she or he.
I'm sure there are complex ways to compose a sentence that renders something such as "She is a man." Or "He is a woman." Etcetera. But that's far beyond the scope of this example. ;)
Én férfi -- I (am a) man.
Te férfi -- You (are a) man.
Ő férfi -- He (is a) man.
Ő nő -- She (is a) woman.