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we got various lectures about how making new friends "their own age" was good for children's social development, only playing with older children was a sign of immaturity, etc....

Well, then, I'm staggeringly immature, as I married a man 8 years older than I am, and many of my friends are ten or more years my senior. Of course, many of my friends are ten or more years my junior, too, so where does that leave the maturity calculations? I have never seen a real-world setting (that wasn't school-based) where anyone was expected to interact only with those whose ages fell within a given twelve-month spread. This sort of "reasoning" on the part of school personnel is not rational, it is just rationalizing.