It is important to recognize and combat sexism and prejudice in all forms, and this includes androcentric language. The word "man" is no longer completely synonymous with "person," which many dictionaries and writing guides acknowledge.
Many studies show that generic male-oriented language (such as using "he" as the default pronoun) makes listeners perceive a man as the default person, too, instead of a woman or gender-nonconforming person. This perpetuates the notion of men as the norm and anything else as the (potentially deviant) exception and can result in a number of detrimental effects primarily on non-male individuals.
Sexism is incredibly pervasive in society, so it is therefore essential that all people do what they can to eradicate it.