I used to be able to throw a ball with either arm ... a passable fastball with my right arm, and a reasonably accurate sidearm with my left. However, last year I tore the hell out of my left rotator cuff while playing Ultimate. It didn't heal right, and I can't move my left arm in the same ways.
So now when I throw left, say when tossing a tennis ball, I don't use much shoulder power. I hold my forearm vertically, then snap forward at the elbow and flick with the wrist. The result is a short, arching, slow toss¹. Conversely, from the right side my power comes from hip and shoulder, with the elbow and wrist employed for guidance and control, not power.
The way I now throw from the left is akin to the way an untutored person might toss a ball, and in fact is the classic "throws like a girl" delivery. Almost any guy my age would so categorize my delivery instantly ... we learned the phrase on the playground and in gym. Maybe this phrase will die out as the public school curriculum changes to give both genders the same sports training.
By the way, last year I taught a female colleague to throw a baseball, and she can now throw home from second as well as, or better than, I can.
1. North American sense.