More specifically, why do they hold only Northern Ireland, and not like, either none of it or all of it?
I don't want to sound obnoxious, but for future reference it's the United Kingdom that holds onto Northern Ireland, not Great Britain. Great Britain is the name of the largest island in the British Isles, which includes England, Scotland and Wales but strictly not Northern Ireland. The UK, however, is the name of the sovereign nation, which does include Northern Ireland (the official name of the UK is in fact the United Kingdom of Great Britain and Northern Ireland).
In response to your question, I can't really add anything that /u/together_apart hasn't already said (apart from the fact that the Great Famine took place between 1845-52 not 1945-52), but tl;dr because Northern Ireland is majority Protestant, as opposed to the rest of Ireland which is majority Catholic, and many of these Protestants are actually the descendants of settlers from Scotland, and hence identify more with the UK than with the Republic of Ireland.
This is actually a very complicated question with a very complicated answer. I'll answer as best as I can.
Firstly, Ireland has a long and complicated history with England as a parent state. The Great Famine (1845-52) is perhaps the best example of the latent and long-standing discontent in Ireland with English rule and although much of the blame regarding that particular incident should be laid with Irish landowners, mostly the ruling English government is held responsible.
Irish independence as a concept had been growing in popularity for many years leading up to the war, and many rebel/loyalist groups had formed, such as: Irish Volunteers (rebel), Ulster Volunteers (Loyalist), ICA (rebel), Cumann na mBan (women's rebel group), Young Citizen Volunteers (neutral then loyalist).
Many Loyalist groups were in fact Irish Protestants, and most rebels being Irish Catholic. The history of these two groups is far too long and complex to detail here. Suffice to say they don't get on.
The Easter Rising was the first major attempt at Irish independence since the 18th century. Carried out by Irish Republican militias, an attempt was made to forcibly secede from the union. They were unsuccessful, with British Army forces halting the uprising within a week.
Although the insurrection was unsuccessful from a military perspective, it brought the idea of Irish independence by force back in to the general consciousness, and it soon became a major political issue on both sides of the Irish Sea.
Throughout the last few years of the Great War, discontent continued to brew in Ireland, with popular support for independence steadily growing - the nails in the coffin being the failure of the Irish Convention reapplication of Home Rule and the disastrous attempt to enforce conscription in Ireland by the Home goverment.
The United Kingdom held Ireland until 1918, with the December election of the Irish Republican party Sinn Féin (by a landslide vote), who formed the [Dáil Éireann](http://en.wikipedia.org/wiki/D%C3%A1il_%C3%89ireann_(Irish_Republic) or Irish Republic on 21st January 1919 and declared independence the very same day.
The Irish War Of Independence is considered to have begun that day, with the shooting of two Royal Irish Constabulary police officers in the Soloheadbeg Ambush being the first belligerent act.
The situation deteriorated quite rapidly. The armed component of the Dáil government, the IRA (Irish Republican Army), formed from several republican militias and began a resistance movement to the British (or more accurately English) denial of independence.
For several months hostilities were fairly limited, but in September 1919 the British government outlawed the Dáil government and ruling Sinn Féin party. The conflict promptly intensified, with more militia forces joining in both sides, a guerilla war arose.
After consistent rebel ambush attacks the British Army was forced into a kind of gradual retreat - although they easily outmatched the republican forces, they couldn't sustain more isolated camps due to constant ambushes and surprise attacks, and they began to lose control of less urban areas.
In response to the wavering control of the Army and Royal Constabulary, the British government formed their own militias from British recruits - the Black and Tans formed to support the Royal Constabulary and the Auxiliary Division formed as a counter insurgency force.
Both groups were formed mostly from British veterans, and became rapidly notorious for civilian reprisal attacks, with the Black and Tans also having notoriously ill discipline. Fighting between the IRA and these groups continued to intensify - with civilians often being caught in the crossfire or paying the price for the other's actions. This portion of the conflict is known as the Tan War.
By 1920 a few hundred people had been killed, but come November the first major atrocity was committed - Bloody Sunday, 21st November 1920.
On the morning of the 21st fourteen British intelligence operatives were assassinated by the IRA. In the afternoon, Royal Constabulary forces opened fire on a crowd at a football match, wounding 65 and killing fourteen. The IRA responded by killing 17 Auxiliaries a week later, and the Army responded by razing the city of Cork in December 1920.
Martial law was declared by the British government in Southern Ireland, but the violence continued to escalate. Some one thousand people died over the next six months, with four and a half thousand interned.
Violence in the North was different from the South and was along sectarian rather than political lines. Having a high Protestant population, resistance to independence was strong and the sectarian nature of the conflict resulted in high Catholic civilian casualties in the region.
The war continued 'till 11 July 1921, with a ceasefire agreed. In May, Ireland was partitioned into the Catholic/Republican majority South and Protestant/Loyal North. With the signing of the Anglo-Irish Treaty, the South was removed from British rule and a provisional government was formed, eventually leading to the creation of the Irish Free State. Northern Ireland remained and remains a component state of the United Kingdom, with a devolved parliament.
The sectarian conflict has continued to this day in some form (known as The Troubles), with the 1998 Good Friday agreement ending much of the remaining rebellious action in Northern Ireland. Most of the remaining hostility is based on the original Protestant/Catholic conflict in the North and that hostility is the basic reason as to why Northern Ireland remained a UK territory.
Some sources:
EDIT: Edit to note I made an edit I forgot to note.. fixed a typo in the Great famine date.