I’ve always worn it on my dominant hand. Dunno why.
This used to be the standard; to be even more thorough, pocket watches - the round thingie on a chain, with the controls on the top - were the standard. Wristwatches were for women.
Pocket watches would generally be generally kept in the left-side of your coat and fished out with the right hand, because 1. your coat would have an internal pocket inside the left breast, and 2. it is easier to find it, and open it, using your right hand, which has better motor control than your left.
So when wristwatches were adopted for men as well, they were now worn on the same hand that previously would have held the pocket watch, the right hand.
Thing is, early wristwatches were pretty delicate. When doing most manual labour, humans have a tendency to hold-still-the-thing with their left hand, and do-the-thing-to-the-thing with their right hand, so if you were hammering something, you'd hammer it using your right hand. The legend was that Polo was a particularly popular sport with people wealthy enough to own watches, and holding the mallet with the right hand while participating in what essentially is medieval horseback melee is not the best work environment for a wristwatch, resulting in an abundance of very expensive, very broken watches.
I'm sure that's at least partly true, but in practice if you work, your right hand tends to get into more trouble than your left, regardless of what work you do.
Also, your right wrist tends to bend more than your left one, for the same reasons. Older watches were bigger and the controls are on the side instead of the top, so they can dig into your hand when you do things like typing on a typewriter.
This whole thingamabob helped move wristwatches to the left, quickly enough that still wearing it on the right was considered something ignorants and fools would do. But, it's more and more accepted to wear them again on the right, if anything most style-conscious people see it as "modern". I used to wear it on the right and have done so for many years, but have grown used to have it on the left, i find it more appropriate to an office setting. I'd probably wear it again on the right if i was still clubbing, idk.