The other thing odd about forbidding the double negative in English is that in Anglo-Saxon, our most direct parent, the double negative served as emphasis, as in

ne beo ge nateshwon deade

You shall (not) not at all die.

In Middle English, sentences could carry double negatives ("he ne lefte nat" for he did not leave) or even triple or quadruple negatives. This was great for Chaucer, who in a negative sentence could practically stick a ne, nat, no or noght wherever he needed a syllable! ("He nevere yet no vilaynie ne sayde...unto no maner wight" means roughly "He never yet said not no villainy unto no-one" but means simply "he spoke ill to no one" or "he never spoke falsely to anyone."

Meanwhile, one of our other close ancestor-languages, French, has the double negative by default. You MUST say ne...pas (or ne...point, ne...plus, ne...personne, etc...) to form a grammatically correct French sentence.

As Rapaire says, it was only when grammarians got hold of modern English, and Latin rules were applied to English sentences, that double-negatives were disallowed. Much as the so-called "split infinitive" was often disallowed, because in Latin the infinitive is a single word. But again, our great writers of yore, like Chaucer and Shakespeare, freely split infinitives, and most enlightened grammarians today allow it as well.