You're trying too hard. You're now saying that there must be exactly one kind of ordering that constitutes ordering, and nothing else can be considered ordered. Or that every ordering must be implemented for a thing to be considered ordered. I'm not sure which you're contending; they're both pretty stupid notions, which is why it surprises me to see you pushing it as a serious argument.

Order has to be imposed externally on the data in the case of arrays too.
No, order is intrinsic to arrays. Not every possible order, but the one that is intrinsic. Any other ordering would have to be imposed. Arrays have one intrinsic ordering. Hashes have zero intrinsic orderings.