He has an excessive appetite.

[Skrej]

My problem is here that In post #1 'an' is necessary but in the post #11 why is 'an' not necessary?

It has to do with whether the noun in question is used as a count or non-count noun.. Compare these two sets of sentences:

A1. He has an excessive appetite.
A2. He has an excessive sex drive.

B1. Women with (an) excessive sex drive are generally termed nymphomaniacs.
B2. Women with (an) excessive appetite are generally termed gluttons.

( Both are true for men as well, of course. I'm just trying to maintain parallel structures for comparison.)

In the A group, the nouns in question is used as a singular count noun, so it requires an article. We need an indefinite singular article, because we're only talking about one non-specific noun. Since the word following the article begins with an vowel sounds, we need 'an' instead of 'a'.

In the B group, the nouns in question are used as mass (uncountable) nouns. However, since they can also be used as count nouns, the parenthetical article is optional. If you consider them non-count, don't use it. If you consider them as singular count, then use it.

In theory, we could treat the nouns in the A group as non-count as well, but it wouldn't sound quite as natural. It's more natural to use it as count since we're talking about the appetite/sex drive of one individual.

 

[Tarheel]

It's #11

I would use "an" there.