Why is it 'an hospital' not 'a hospital'?

Answer 1

Both are acceptable. The letter h was at one stage, due to the influence of French on the English language, considered a half-vowel and was silent and words starting with h were therefore accorded the indefinite article an. In British English this inflence is more or less confined to the history books, apart from the occasional use of an hotel or an historic occasion. In American English the French influence is more prevalent, compare British and American pronunciations of the word herb
It can be both! The letter h is considered a "half-vowel". As a result of the influence of French (where the h is silent) on the English language, words beginning with h were treated as if they began with a vowel and preceeded with by the indefinite article an. As English developed and French words such as hospital, hotelwere anglicised, the h became pronounced and the use of a became more prevalent over the previously used an. Some publications still use the indefinite article an but it is now generally considered archaic.

I've never heard of a "half-vowel," therefore, I can't comment on that. However, how I was taught in school was that you use an if the next word starts with a vowel. I've never heard anyone say, "An hospital" either. It doesn't even remotely sound right. Trust me, it's "a hospital."