A quick googling turned up an article which said something along the lines of - "Back in the old days men dressed themselves, hence the right side due to right handedness. Women on the other hand were dressed by others, so instead it was on the left."
This doesn't make sense to me, surely every woman back in the day didn't have someone to dress her. Does anyone have any real source on the subject?
In Jack Weatherford's book Genghis Khan and the Making of the Modern World he argued that it came from China and had to do with women not being allowed to fight. When drawing a bow right handed you want the opening of your shirt to face away from the string your drawing so that you don't get it caught in it, or at least that was the idea. Buttoning the other way was meant to show that you wouldn't fight because you were a 'civilized' woman. He did cite a few examples of Mongol women being very annoyed about changes in clothes when they were in China but I'm not sure I entirely buy his argument. Possibly worth considering, though.
When did this left vs right difference first started appearing?
The idea that it's because women had dressers is an old myth (honestly, I haven't found the source but it seems almost as old as the rule itself). The separation doesn't occur until the late 19th century. Prior to that, we see most garments being left over right, but a decent assortment with right over left and no discernible trends to it. Women's garments that buttoned up the front were generally considered masculine to begin with and were often made by tailors; ladies riding habits based on men's jackets, pelisses and redingotes on men's great coats, etc. It's not until the 1860s when women's wear begins to commonly button up the front. It's also at this time that the right over left trend begins for women.
I will state there is not an easy answer to this. No single person or designer declared this to be the rule all of a sudden. However, by the 1870s I am hard pressed to find examples of women's garments being left over right. It's also around this time that women begin wearing more masculine style garments and calling them their own. Such as the shirt. Wearing a shirt and skirt was not fashionable prior to that same time. Now adopting a masculine style garment, as well as the masculine use of buttons in front for fastening, they perhaps thought to differentiate through this method. Add in the surge in mass-produced, pre-made, catalogue order style clothing in the late 19th century and this would easily become "standard" production.
It is most definitely not, however, due to being dressed by maids. Men were dressed by servants as well. It's not any easier to fasten it one way or the other. I can comfortably do both on a person or on myself. It's also not a sign of wealth, because if they wanted to show they were being dressed by a servant the gowns would only fasten in back, making a servant necessary. There also isn't any evidence that it's meant to be degrading. It's just buttons, not a political or social statement.