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.
If you think about it, you’ll see how little sense it makes. Back before things like cars, motels, and telephones, having an affair was complicated. You couldn’t just pop over for a quickie. On the other hand, servants were cheap. Even a cop or a school teacher could afford at least one maid.