In the past, almost everybody travelled on the left side of the road because that was the most sensible option for feudal, violent societies. Since most people are right-handed, swordsmen preferred to keep to the left in order to have their right arm nearer to an opponent and their scabbard further from him. Moreover, it reduced the chance of the scabbard (worn on the left) hitting other people.
Furthermore, a right-handed person finds it easier to mount a horse from the left side of the horse, and it would be very difficult to do otherwise if wearing a sword (which would be worn on the left). It is safer to mount and dismount towards the side of the road, rather than in the middle of traffic, so if one mounts on the left, then the horse should be ridden on the left side of the road.