Both my parents are ambidextrous, I'm not - why?

My mother was actually left handed but was encouraged to write with her right hand as a child, but in adulthood her handwriting with either hand was excellent although she did use her right hand more often.

My dad's teacher was amused to see how he wrote things on the blackboard when asked - he'd start writing the sentence with his left hand and when he got to the middle would transfer the chalk to his right hand and continue until the end. This somehow seems easier to do on a blackboard than when writing on paper (I've tried this myself and it's not too bad).

But my handwriting with my left hand is pretty bad - why am I not ambidextrous? And can I improve my left hand writing with practice? 

I've been remembering my non-impressive attempts to take up archery a year or two ago (fun, but don't rely on  me for your dinner, I might hit the animal but unlikely to be a clean kill) and how being left-eyed and right-handed turned out not to be that brilliant a combination.