Why is it wrong to say 'an university'?

Recently a student asked "why can't I say 'an university'?" She had learnt that any noun starting with a vowel (a, e, i, o, u) should us 'an'., but now she was being told 'an university' is wrong!

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In beginner English lessons it is taught that if a noun begins with a vowel (a,e,i,o,u) it uses 'an', and if it uses a consonant (all the letters which are not vowels) it uses 'a'. However, this is not actually correct.

“ It is how the word is pronounced that determines whether you use a or an, not the actual first letter of the word .”

Say the word 'University' out loud and listen to the first syllable. Now say 'umbrella' out loud. Can you hear the difference the way the 'u' is pronounced?

Rule

Use 'an' if the first letter of a word is pronounced as a vowel sound.

Use 'a' if the first letter of a word is pronounced as a consonant.