Why Sister States / Circuits / Cities and Not Brothers?

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My friend Josh Bornstein asked me a question related this, and I realized I knew the custom but not the reason. At least in court decisions, states are always "sister states" and never "brother states," and likewise with circuit courts—except, as it happens, in Louisiana, where "brother circuits" and "brethren circuits" does appear (though still much less often than "sister circuits"). Likewise, in popular usage we have "sister cities" but almost never "brother cities."

But why? I assume it flows from broader customs, perhaps the historical references to nations as "she." But where did that come from? I crave enlightenment.