Why does a woman walk on the left of a man on the street?

A woman walks to the inside of the sidewalk, away from the street where there is less danger of being splattered by passing traffic when the streets are wet. Also, in the old days in some countries, people threw their garbage (among other things) out of apartment Windows into the street and the person walking closest to the building was less apt to be hit. That was what I learned from etiquette books when I started dating.

In modern times, it gives her a chance to window shop.

Also, in older times, men wore their sWord on the left hip, to be drawn with their right hand. Men therefore had to pass each other on their right sides to avoid clanging their sWords together, and also to keep the sWord away from any passerby that might be a potential enemy, to keep them from attempting to grab the sWord. Having one's lady on the left arm also had the advantages of shielding her from said potential enemy, allowing one to press her away from danger, and also keep the sWord arm (right arm) free to draw the blade at a moment's notice.