Why are things left-right reversed in the USA?

Everyone knows that in the USA you drive on the right, whereas in England you drive on the left.

However, I was surprised the first time I sat on a bicycle here: the brake levers are reversed. The right lever operates the back brake, not the front. (I’m glad I noticed before trying an emergency stop.)

Now I’ve discovered a third and even more bizarre left/right inversion: zips. (Or zippers, if you prefer.) This month I bought a new coat, and discovered while trying a few on that American jackets have the movable part on the right hand side of the zip fastener, as you view it while wearing the garment. So instead of grasping the zip with my right hand and fastening it with my left, I have to get used to the reverse.

Can anyone explain how this came to be? Who decides these things?

I remember that in England, men and women’s clothes button up in opposite directions. For a man, the buttons are on the right. Does this mean that American zip fastener manufacturers are treating the movable part of the zip as an honorary button?

It seems reasonable. Yet that implies that English men’s jackets zip up like a girl’s buttons. Come to think of it, that would explain a lot…