It is about the metaphor, and the metaphor is illustrating the choices women have in many situations: politely decline and show my independence and walk through my own set of doors, or take advantage of the opportunity to have someone do it for me (and then write an article about sexism about it later).
I’m not suggesting that there isn’t blatant sexism in the world, because there is. But I do believe that a lot of women are not treated equal because of their reactions to the perceived “microaggressions” they encounter every day. If you didn’t want to change the direction you were walking (metaphor for giving into a man’s wishes) then you should have kept walking. But you chose to change your path. And you chose to wait for him to catch up, rather than just saying, “No, you got the last one, I’ll handle this.”
Or was that not the metaphor?