Men’s buttons are on the right to make it easy to do up with one hand for right-handed people.
When buttons were invented, only the wealthy wore them. Wealthy women had maids who would do the buttons up for them, and so the buttons are on the left so that they are easier for someone facing you to do up.
Yes, most men are right handed, and most maids who helped women dress in the past were right handed.
This whole sentence could be summed up as “humans are mostly right handed”.