I'm sure that also became a consideration when I was young since horses by then were long gone except for around Central Park.
In NYC you have the potential danger of a car going out of control and going into the sidewalk, therefore the man should be closest to the street.
She also insisted I carry a handkerchief with me at all times. I found out later in life that was due to the Spanish Flu epidemic of 1918. (Sorry Trump it did not happen in 1917 you dumbass.) She had 6 children and she kept them all in the house for a year and they could only go out if they were wearing a handkerchief around their face.
Even today I still carry one around with me daily.