Hrrm, this is only half remembered so there will be mistakes no doubt.
Sinistere was Latin for left and is where we get our word for sinister, thought they didn't use it as we so.
Leftiness was associatede witht he moon and femalehood and when the Church took over was corresponded in kind with paganism in the form of lunar deities and satan.
Other than that, I know there are sexual connotations associated with the left hand in Hinduism and possibly Buddhism too.

Maybe a topic in the Monastery is in order, they know an awful lot in there!

Oh and my case is funny, I use both hands but am not ambidextrous as if I do one thing with one hand, I usually can't do it with the other. Like I write with my right, but fence with my left.