I've been thinking about this one a lot lately- not sure everyone does and maybe if you live where it's mostly straight or have wide sweepers it's not so much of an issue.
But here in twisty land it's an important distinction. So, why are right hand turns more dangerous? I can think of four reasons...
1) The same turn is inherently sharper for you than it is for oncoming traffic, as you're on the inside.
2) Your site distance is more limited because it is sharper. This is especially true in tight twisties with vegetation and/or a mountainside blocking your view through the turn.
3) Oncoming traffic uses left turns to "cut the corner." I followed two cars today that routinely straddled the center line whenever they were coming into a left turn. Only when they saw oncoming traffic did they get over, and not always all the way!
4) There's a fourth reason and it escapes me. I'll come back to it. Someone else fill it in....
I guess it may have been that, as
@1olbull said, by swinging wide for a better view and angle into the turn it puts you closer to the centerline which, apparently, is not universally accepted as a division between opposing traffic.