Because noun starts with a vowel. Usually when a word starts with vowels (a,e,i,o,u) then we use the article an

You can either say: 'I don't have much appetite' or 'I don't have much of an appetite' You cannot simply drop the 'an' - it's not possible to say 'I don't have much of appetite.' Note that this fixed pattern can be used with other objects. For example: You don't have much chance. You don't have much of a chance.

Hi Ali, that's how the idiom/expression is -to have AN appetite-, if you say "I don't have much of appetite", it's wrong.

I agree with the two other answers and just wanted to add that you could also say "I don't have much appetite" (without an article AND without "of"). However, if you say "of," you need an article. Similarly, you could say both "I don't have much money" and "I don't have much of the money," both "I don't have much interest" and "I don't have much of an interest," and both "I didn't eat much cake" and "I didn't eat much of the cake."