Yeah I think it amounts to society being optimized for the majority (right-handers, extroverts, theists, etc). and the otherizing of the Different. I'm sure the battle anecdote and a thousand other little examples are in play. I'm sure if you're training a soldier and they don't hold the battle axe in the CORRECT hand (I wonder if it's a coincidence that "right" = "correct" ) then they're doing it "wrong" and are trying to be some kind of wise guy.

I think it even used to be a "thing" that parents would unintentionally traumatize their children by trying to prevent them from exhibiting left-handedness. We were (and to a tragic extent, still are) a very conformance-biased society and so even if the parent didn't personally care, they probably had some well-meaning concerns about how it would be a lifelong burden for the child.

Thankfully we're gradually moving past all that but we have a long way to go. There are other manifestations of neurologically atypical characteristics of which left-handedness is simply a mild example, and the more tolerant society becomes of different ways of being, the better.

[getpocket.com]

here is an insightful look at left handedness...

It is certainly mainly prejudice, two theories are, that it is just a prejudice against left handed people simply because they were seen as different, in an age of little travel and closed minds when people thought that just being different meant that you were cursed or a devil associate. The other comes from misogamy because it was the custom to put the female half on the left hand side on coats of arms and family trees.