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"yyyy-mm-dd" and "dd-mm-yyyy" are both sorted - one descending, one ascendig.

"mm-dd-yyyy" is just an arbitrary bag of entities, and a part of the population memorizes the order of them.

It's not completely arbitrary, it matches the way we write out full dates or speak then aloud. January 2nd, 1900 becomes 1/2/1900.

Totally arbitrary. In French 2ème Janvier 1900 would be the most common.

I mean, it's no more arbitrary than any other order. In the context of "why does American English use this ordering", it has the desirable characteristic that it matches how we express dates in our everyday language. A trade-off exists between that characteristic and the desire to have the date go from smallest to largest or vice versa, but both approaches have practical benefits.

That is also arbitrary.

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