Kind of feel like preference probably comes from a compounding effect of practice. One starts learning how to do simple things with a chosen hand as a baby and as one tries to learn more complicated things they develop an ever-growing preference to use the one that'll necessitate less practice for the new skill due to already having some practice.

As for which hand is chosen as a baby, it might be most typical to mirror one's parents, but it doesn't always have to be like that. Some babies may just randomly start doing things with a hand different to the preference of their parents due to not having them or other adults in their sight at critical moments. As for parents trying and failing to stop their kids from using their left hand, they might've just caught it too late.

So, I guess what I'm saying is that both you and GP can be correct.