Why women hold the left arm of the man when they walk in?

This tradition was started by the middle Ages, when men were accompanied by their ladies in the city and in the fields. The times were difficult and they had to be prepared just in case.
In the case of a well, resulting a threat to defend the honour of their good, just removed the sword from its sheath (located on the left side) with their right hand, for greater convenience. So in simple words, the left hand remain free for the ladies.
Until today, the tradition of the left arm force, but only when it comes to interiors.
The reason is simple: cars. With the increase of vehicles and the roads, and the proper etiquette of the escort of ladies has evolved.
Today, so when someone accompanies a woman in the outdoors, must be located from outer side, closer to the road in order to protect it from vehicle traffic, the dirt, the water, the splashing etc.