As for grammatic correctness, well yes strictly speaking it is incorrect, but who defines what is right anyway? The ultimate arbiter of what constitutes "correct" grammar is usage after all. And getting round this gender identification problem by the use of plurals is becoming increasingly common in everyday speech.
"He" or "man" in English serves as both indicator of male gender and a generic reference to a human being of unknown gender. "He or she" is not only clumsy, it is illiterate. Use "he".
The ultimate arbiter of what constitutes “correct” grammar is usage after all.
Congratulations; you agree with the eminent linguist, Noam Chomsky.