Whole thing is real complex.
Hundreds of years ago, countries were forming, and in many many cases, smaller countries were taken over or merged with other small countries to make slightly larger countries. We're talking about a time when "diplomacy" meant "Who had the biggest sword". It happened all over europe, leading almost to the boundaries we have today. In a way a bit like how the United States became - note what happened last time some stated wanted to leave
England had taken over the smaller warring English kingdoms quite early, and had become the more developed country in the area. For political reasons, the focus eventually turned on the fringes of England - the celtic areas, which by comparison were very undeveloped, and in the case of what's now Wales, fractured into petty kingdoms still.
When Ireland became part of this new "country", an attempt was made to introduce "more loyal" protestants into what was a largely catholic leaning land. Thus began a Scottish invasion - something which even today can be seen in various sectarian ideas. The English as a whole have no time whatsoever for ridiculous sectarian rubbish, but it's a big issue in Scotland.
So why didn't Ireland become like Savoy, like Normandy etc and part of a united country? Well, look again to history. For part of an alleged united one country, the Irish were treated very shabbily by the English dominated country.
Even as recently as early last century, most Irish would have been happy with some devolved self rule, under a united monarch, but more and more, independance became the more attractive option.
This happened in the 20's. Interestingly, it's a bit "must not say" in Ireland even today, what happened immediately after independance. Bosnian style massacres and oppression by Irish of Irish, and many must have thought would things ever get better. Bit like the other "must not say" - the real sympathies by many Irish in government during a nominally neutral country during WW2.
When Ireland got independance, the UK government allowed a vocal protestant minority to do some "tail wagging of the dog". Part of Northern Ireland remained in the UK.
This was a cause for grievance and resentment. Sectarian sabre rattling became so intense during the late 60's/early 70's that the British army was sent in - originally to prevent a wholesale massacre of catholics by the protestant militias. It's an interesting twist of history that many in the IRA would not have been around had it not been for the UK army protecting them - they'd have possibly been killed.
Originally welcomed by the catholic population, it wasn't long before this army was seen as an army of occupation, then began the long campaign of terrorism on both sides (And don't forget, one mans terrorist is another mans freedom fighter).
Not going to go into who is right and who is wrong - frankly after this amount of time, it's hard to say just who is.
The UK for a long time has wanted out of Northern Ireland, but cannot as it would be abandoning a land where most people wanted the status quo, due to "terrorist" activities. Certainly most people in the UK were heartily sick of Ireland and were of the opinion "f*** them, lets get out, they want their heads banging together".
The uk isn't China, if Ireland wanted to be united, the UK would be right out of there. It's big mistake was by not saying 90 years ago "Bye" to ALL of Ireland.
Frankly, the whole thing is pathetic, too many people who just can't get along, and who are totally oblivious to the fact that since we're all in europe anyway, who cares whose tatty little flag is flying over a public building.