Time for a factual lesson lol
Here's how it goes:
Great Britain (also referred to as the mainland) consists of Scotland, England and Wales.
The United Kingdom (Officially may be shorted to Britain
but not Great Britain) consists of Scotland, England, Wales and Northern Ireland.
The
British Isles consists of Scotland, England, Wales, Northern Ireland, Republic of Ireland, Isle of Man and the Channel Islands.
When Ireland got it's independence from Britain, Northern Ireland opted to remain as part of the UK. The majority of inhabitants in Northern Ireland still want to remain as part of the UK today. A minority do not and hence the formation of terrorist groups such as the IRA, to make Northern Ireland independent by use of terrorist force.
Since Northern Ireland remains as part of the United Kingdom, it's inhabitants are therefore British in nationality. Just in the same way that a Scottish, English or Welsh person is also British. You don't have to be born or live in the mainland to hold British nationality. You can be born anywhere within the British Isles (with the exception of the Republic of Ireland which is now independent) and hold British nationality.
BTW I am not having a go at you, so apologies if my post comes across that way.