Is this correct grammar?

It is used before an initial vowel sound and sometimes before an initial unstressed syllable beginning with a silent or weakly pronounced “h”.

Examples include: an honour an hour an historian (However, “an history essay” is incorrect grammar; it’s “a history essay”).

The correct grammer( assuming you are in England) is than A goes before a constanant and AN goes before an vowel Anything else just isn’t cricket!

The real answer is that the English language is constantly changing, and your dad is applying correct but out-of-date rules. No one has changed the rules yet, so he is right, but almost no one sticks to them any more, so your history teacher (whilst a bit thoughtess not to explain) is probably just encouraging you to use modern English instead of something old fashioned. The rules are changing as we watch…

The historical reason for the ‘an’ in front of many ‘h’ words is that ‘h’s are all silent in French, so once upon a time the words we borrowed from French like ‘hotel’ or ‘history’ were pronounced without the ‘h’ sound. Odal’s summary of how the rules currently work is pretty good, but also going out of date. The rules will probably catch up with modern usage in your life-time!

Use “a” before words beginning in “h” if the “h” sound is pronounced.

e.g. a history, a hero, a home, a heart

Use “an” before words beginning in “h” if the “h” sound is NOT sounded. (h sound is silent.

e.g. an hour, an honor