Why Sister States / Circuits / Cities and Not Brothers?

Josh Bornstein, my friend asked me this question. I realized that I was familiar with the practice but not the reasons. 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”). In popular usage, we often use the term “brother city” instead of “sister cities”.

Why? It may be a result of broader customs or historical references to countries as “she”. I wonder where that came from. I crave enlightenment.