I don't know about what happened to you personally, but that's a pretty common type of bicycle accident which can produce quite serious injuries.
The issue is rolling off the edge of the pavement and trying to steer back. Oftentimes there's an edge on the side of the pavement. If you try to roll over that edge at an angle, your bike will tip you over to the left.
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My greatest fear is all of my kids standing around my coffin and talking about "how sensible" dad was.