Why do some authors use the word an before all words that start with an H? Is this form of writing correct?

Contemporary writers using American English generally follow these basic rules for using the indefinite articles and an:
  • Use a before nouns starting with a consonant (a boy, a cat, a donut).
  • Use an before nouns starting with a vowel (an apple, an elephant, an ice cream cone).

Exceptions:

  • For nouns beginning with a silent-h, use an (an hour, an honor, an honest man), but if the h is not silent, use a (a horse, a handle, a heart).
  • Use a before nouns beginning with u and eu when they sound like "you" (a European, a university, a unit).

Writers of Early Modern English applied an more widely to words beginning with h because speaking patterns of the times made that initial letter silent in many words, such as an heroic act.

Now that the once-unspoken letter h is being heard in our modern-day language, use of an is becoming increasingly rare with harsh-h sounding words. An occasional an historical, an hereditary, or an hysterectomy may creep into formal writing — or even everyday conversation — but these dated references are going out of fashion.