Women influence from behind, not of their own free will and not on purpose, it is created by nature. It's just that in a woman, the muscle in the perineum is located across, so when walking, she tightens the gluteal muscles and the illusion of the hall wagging occurs. In a man, the muscle is located along the perineum and therefore this effect does not occur. This is connected with the fact that a woman in sex, in bed, spreads her legs more freely
Why is someone slouched over? Why does a man waddle or sit with his legs wide apart?
Either physiology (wide hips and protruding buttocks will "wag" with any gait), or it is a habit (like waddling gait or shuffling feet).
As for "intention", then it's difficult here. Some girls try (!) To wiggle their hips, because men sexualize such a gait (although initially it is neutral - everything is in your heads), believing that in this way the chosen partner might like them.
On my own behalf, I would like to emphasize once again that since gait is something that can be controlled, but still rather difficult, the girl will somehow involuntarily return to her usual walking style.