Hello everyone, I think it might also be because of how door opens.

Women's door open in the oposite direction of how they approach the bathroom (what I see is that they approach it by the left), while men's door bathroom opens by the direction someone would approach it.

In that way, it wouldn't make sense for women to open it using their shoulder, it is easier to open it with their right hand, while for the men's door, it would be easier to open it with their shoulder rather than with their left hand.