I am a lefty. ...Robert Plant, Jimi Hendrix, Ronald Reagan.. all Lefty’s

I truly don’t consider Throwing Lefty but batting Righty the ‘opposite’. Call me crazy (which I am) ... I have always believed that your primary eye was a key factor in determining whether you would feel more comfortable batting Lefty vs Righty at a young age. Batting from the right side allows you to track the ball better with your left eye.
I did assimilate certain things....for example scissors righty (and batting I guess). I also use a screw driver etc with either hand. But throw a frisbee much better righty.