From an etymological perspective, this viewpoint is false. "Man" has never been exclusively gender-neutral in English. While the Oxford English Dictionary does include meanings of "man" that are gender-neutral, some of which now obsolete, it also shows that this same word has referred to male persons from the beginning, too.
Even in Proto-Indo-European, the ancient ancestor that gave English most of its words, the word for "man" refers mainly to a male person.
Words like "mankind" have thus never been completely gender-neutral, rendering this argument invalid.