I think we agree, at least in part. The problem is, as you say, that unrighteous males do pressure women. Women are spoken of scripturally as 'weaker vessels' and men are to protect and defend them.
Headship includes protection from harm and also has a self-sacrificing aspect, the Shepherd willing to die for the flock and the man willing to die to protect the woman. That kind of man gains a woman's love and respect and she gladly submits to (follows and supports) his non-bullying leadership.
Vastly different from the bullying, coarse wife-beating rogue that is all too real in many women's lives.
Good point.
I realize that men have an instinct to protect women. However, I don't see how this relates to the original thread of the Pope asking engaged couples to remain chaste. You seemed to imply in your post that men are the guardians of women's chastity, which is nonsense. While men naturally desire to protect their wives or girlfriends from other men, that does not mean that they act as the protectors of chastity within their own marriages or relationships.
In the case of dating or engaged couples, it is generally the woman who sets the sexual tone of the relationship. If she is permissive, then the man will take liberties. If she values her own virtue, the man will generally go along with her. The man's desire to "protect" her just doesn't figure into this situation nor does the notion of headship.