May I direct your attention to
Man | Define Man at Dictionary.com and the three meanings quoted below.
man
1 /mæn/ Show Spelled [man] Show IPA noun,pluralmen, verb,manned, man·ning, interjection
–noun
2. a member of the species Homo sapiens or all the members of this species collectively, without regard to sex: prehistoric man.
3. the human individual as representing the species, without reference to sex; the human race; humankind: Man hopes for peace, but prepares for war.
4. a human being; person: to give a man a chance; When the audience smelled the smoke, it was every man for himself.
The proper definition of the word is pretty clear in that it can properly be used in both ways. To argue that it is incorrect to use man in the context of females is simply being PC just to be PC.