Nothing to do with this. White men running NASA, white men running the Air Force, white men running the show could not and would not have a woman beat them to space. End of story. It's pure discrimination. It was widely known that physiologically and psychologically a woman is better suited for space flights. It was just ignored. Just like the claim "they can't fly", in WWII many women pilots proved that they could do the work as well, if not better, than their male colleagues who were busy with things "more important".
Don't forget that the same was true for black and hispanic astronauts. First black astronaut? 1983. First woman astronaut? 1983. First hispanic astronaut? 1980 (Cuba on Soviet flight), 1991 (first American born hispanic astronaut), 1993 (first American born hispanic woman astronaut).
It's all about white men.