The issue here is the difference between British English and American English and to a lesser extent Canadian or Australian English. In many parts of Great Britain, the "h" is silent or very very soft, pronounced "otel", so "an hotel". In America the "h" is pronounced so "a hotel". In America most nouns that start with "h" use "a". A house, a hurricane, a hotel, a horse, a home, etc. The only exception that I can think of the the word herb. Most Americans (at least in the North East ) pronounce it "erb". So "an" is used. For example: that plant is an herb.
Both "an hotel" and "a hotel" are correct depending on where you live.
"[...] Today, though, these three words are generally pronounced with a spoken ‘h’ at the beginning and so it’s now more logical to refer to ‘a hotel’, ‘a historic event’, or ‘a horrific accident’."
It depends a bit on where you are in the world. Where I live we say 'an honor to meet you' but we say 'a hotel.'
You should come over to the Portuguese tree and see what passes for "English" there... truly hair-raising! ;-)
Whether the 'h' is aspirated or not, good English remains "an hotel" - "a hotel" is poor English and should not be used in a language course!