Two other answers from the internet:
Hundreds of years ago, women were dressed by their slave/servant/handmaiden/lady-in-waiting. Men usually dressed themselves.
And because most people are right-handed, it's easier to button a garment if the button is on the right.
The placement of men's and women's shirt buttons, left or right goes back to where the buttons were originally placed on the garment, front or back. Men's clothing always buttoned in the front and the buttons were set up to give a right handed man the easiest way to button his shirt. Women's buttons were originally placed in the back. They therefore had to have someone button their buttons for them. In order to make it easier for the person buttoning up the woman, the buttons had to be placed on the left instead of the right. By the time women's buttons were place in the front of the garment, women's clothing makers were already accustomed to placing the buttons on the left hand side