I'm pretty sure you're supposed to wear your watch on your left arm if you're right handed and on your right arm if you're left handed. Maybe that's why most wear it on their left because of how most people are right handed?
Left, it's what my father told me It's because like this you can put the right hours on your watch. I don't know how to explain it since I'm bad at English. Just watch this pic and I hope you understand what I tried to said.
Both men and women should wear it on the left. But with women the side with the face of the watch shouldn't be facing outwards but inwards towards your body. I don't know why, just one of those things that don't really have a good reason. And because of that i wear it however i want to.
It goes back to old fashioned watch with winder - Most people are right handed correct - On left wrist winder is at the most easy accessible position for dominant right hand - It just never changed when watches went digital or battery