I don't know for sure, but I suspect (in keeping with the fetishization of Latin that motivates many prescriptivist rules, like the injunction to never split an

I don't know for sure, but I suspect (in keeping with the fetishization of Latin that motivates many prescriptivist rules, like the injunction to never split an infinitive) that this arises from Ancient Greek[0], wherein there is not a separate letter "H" but rather a modification ("breath", if I remember rightly?) on the vowel. If you (mis)apply this rule to English, "hospital" starts with a vowel. [0] this might be true in Modern Greek as well, I don't know - but English professors don't have such a raging boner for the modern version.