"an" and "a" are the same except "an" is used when the noun begins with a vowel. e.g an accident, an eclipse, an institute.
This is not correct- it's about whether the word after it begins with a vowel
sound:
An egg
but
A European
An umbrella
but
A university
Also note:
An MA
A URL
And it's triggered by the word coming after it, so it doesn't have to be a noun:
A student (noun)
but
An average student (adjective + noun)
An extremely good student (adverb + adjective + noun)
And this "rule":
We say an hour, an hotel but we write it with an "a"
According to you, we would write[strike] a hour[/strike], which is wrong. We write
an hour. Some people use
an historic..., and plenty of those who do pronounce the /h/. There are various possibilities with
h, but teaching people to write [strike]a hour[/strike] is not one of them in my book- this would be marked wrong in an English language exam.
And how about
humorous? According to you, we'd say
an humorous and write
a humorous. If you did try to make the
h silent, you'd have /j/ at the beginning rather than /hj/, so even dropping the
h, your theory on the pronunciation still breaks down.