Why is it "a Korean" but not "a British"?

We can correctly say a Korean, an American, an Indian etc...

but not "a British"?

(I am Korean/I am Korean = both fine..
(I am British = fine. I am a British = incorrect)

Also to add....I suppose "Korean" can function as an adjective and a noun...but English cannot.

The difference between the word endings -an.....and -ish (and -ese for that matter) must be the issue here. But I don't fully understand it. I am American, I am an American - correct....I am Japanese, correct...I am "a" Japanese - incorrect.

Brighter minds than mine please help~!

When we talk about the United Kingdom (UK), English is not the same as British. English is not used for Scottish or Welsh or Northern Irish people. (Great) Britain refers to the territory of England, Scotland and Wales. The United Kingdom refers to England, Scotland, Wales and the six counties of Northern Ireland. Some people from Northern Ireland refer to themselves as British in the context of the United Kingdom of Britain and Northern Ireland. However, everyone from Northern Ireland has the right to Irish nationality and can hold an Irish passport. Irish also refers to citizens of the Irish Republic.

The Scots themselves prefer the adjective Scots and it also occurs in the compounds Scotsman and Scotswoman. We use the adjective Scotch to refer only to food and drink from Scotland e.g. Scotch broth (broth is a kind of soup).

I am a Briton. Can be informally shortened to "Brit".

In light of the OP, would you feel it normal to refer to yourself as "a British"(full stop)?

In light of the OP, would you feel it normal to refer to yourself as "a British"(full stop)?