IOW, why handed vs ambidextrous, not so much why left-handed vs right-handed.
Did it even explain that? I'm ambidextrous, I have no handedness bias, so whichever I pick up to first learn something is the hand I use. So I'm a mix of left-handed and right-handed depending on the task. And yet I didn't really understand why that's odd because of my bipedalism?
Mildly informative Wikipedia article: https://en.wikipedia.org/wiki/Cross-dominance
I'm right-handed. I'm definitely sure of that. It's just that what hand I use depends on which hand I start with from the beginning. And that'll be the preferred hand, except for things where it's natural to switch from the very beginning.
But there are also some things I've learned to do with both hands much later, e.g. washing dishes - there was a reason for having to do that for a while, and now I just switch when I like it, or if the kitchen happens to be arranged in a way which makes one side more preferable.
(BTW, when building carpenters still used common hammers it was completely normal to use either hand, as access space may be limited and there's basically no choice sometimes.)
may be high dexterity is expensive, brain-wise, i.e. may be the choice given average brain is either 2 hands with mild dexterity or a one of high dexterity at the expense of the other. With tools, etc. the latter choice seem to be preferable and was selected for (and the lucky ones get to have 2 of high dexterity) Bipedalism and brain expansion in this situation are indirectly connected to the handedness as they are enablers and drivers of tools use.
Neither of my parents were left handed, and yet, here I am; despite attempts otherwise I might add.
For example, throwing (or kicking) with your non-preferred side is not as simple as picking up and throwing a ball or simply kicking it. You have to adjust your position and stride to lead with the correct foot. I found learning right-handed pace bowling in cricket (for fun) especially challenging as you have to land your back foot in the right place as you bowl through the popping crease. A few steps and rolling the arm over to spin was easy, and I actually can get more spin on the ball with my right hand.
My theory is that the handedness came about through learning basic survival activities such as running and jumping, throwing spears or rocks, etc that require using a preferred or learned hand.