There are many possible explanations but I think it has something to do with practical things.
Polish knights and later nobles wore their swords (later sabres) on their's left side. If bride was on that side it would be uncomfortable and possibly dangerous.
Not at all: swords were kept in sheaths for a reason.
The reason for keeping a woman on one's left is because one will want a person coming towards one to pass on one's right, so that if one needs to defend oneself (and one's fair lady) the attacker is on one's sword-arm side (the same reason why one rides a horse along the left side of a path/road) and not on the side where the fair lady is. It is not generally considered chivalrous to use a lady as a shield against one's attacker.
The allegedly Polish tradition was actually first introduced to Poland by the Teutonic knights who, as primarily defensive in nature (allegedly), showed this by walking on the left side of a woman so that they could raise their shield and use it if she needed defending.