nouns - Why can we say 'an American' but not 'a British'?

I am confused with the use of an indefinite article in front of British or Chinese.
To my understanding, we can place an indefinite article in front of any “countable noun”.
So, we can say a cup and an orange.

But when it comes to nationalities, it is very confusing. For example, we can say an American or a German. But we cannot say a British or a Chinese.

I looked them up in a dictionary as at first I thought British and Chinese are adjectives in the above statement and that is why we cannot place an article in front of it.

However, the dictionary mentions that they are nouns. Does that mean they are uncountable nouns?