From the comments I see we can omit "yo" and just say "soy un hombre", and we can also omit "un" and say "yo soy hombre". Is it permissible to omit both simultaneously i.e. "soy hombre" ? Would that have the same meaning? Any different connotations?
I am Hungarian and in my language it is also possible to say this in both ways. Here there is only a tiny difference in meaning. Without the indefinte article there is more emphasis on the noun (man), and perhaps a stronger endorsement of the fact.
EXACTLY!!!, it is almost the same but its not always exactly the same, when you omit the article the noun is stronger and it gives a stronger sense of not so much what you are but how strong it is, like "i a MALE" "im all mAN" 'Im masculine".