Just as the British failed their objetive which was to keep the whole island.
That's a simplistic and ignorant way of looking at things. Things were a lot more complicated.
The British were seeking Home Rule for the whole of Ireland within the United Kingdom, something which the majority of the Irish wanted. Most Irish at this stage did not want to secede from the UK and were content with Home Rule within the UK.
However, the Ulster Unionist Party (UUP) opposed Irish Home Rule and formed their own militia, the Ulster Volunteers, opposing it. The Irish nationalists, in turn, formed a rival militia, the Irish Volunteers, to fight for Home Rule.
The UK Parliament was about to pass a Bill for Irish Home Rule but this was suspended temporarily when WWI broke out in 1914.
The Irish republicans were also opposed to Britain's involvement in the war against the evil Hun and even colluded with them, with the Hun providing them with weapons.
On 21st January 1919, after Britain's victory in WWI, Sinn Féin formed a breakaway government in Ireland and, later that day, the IRA shot dead two police officers. This is often seen as the beginning of the Irish War of Independence, with the IRA attacking police officers and British soldiers. It was during this conflict that Irish public opinion turned away from Home Rule within the UK and towards full independence, shocked as they were at some of the mass killings committed by British troops (despite the fact that the IRA were, themselves, very good at mass murder atrocities). However, there were many Protestants in the north of Ireland who opposed Irish independence. The Irish War of Independence therefore ended in 1921 with the Anglo-Irish Treaty, which provided for the creation of an independent Irish Free State as a self-governing dominion within the Commonwealth (the first use by the UK government of this term, rather than "British Empire", in an official document). It also provided for Northern Ireland, which had been created in 1920, to opt out of being part of the Irish Free State. It took the decision to remain separate from the Irish Free State and remain within the UK.
The Irish Free State became a republic in 1949 - the Republic of Ireland. In the same year, it also seceded from the Commonwealth.
Of course, the Irish republicans were outraged at this and wanted Northern Ireland as part of the Irish Free State and so the Irish Civil War broke out in 1922. This was fought between the pro-Treaty forces of the Irish Free State (which were supported and heavily armed by the British) and the anti-Treaty forces. The civil war ended in May 1923 as a victory for the pro-Treaty forces.
Hence why Northern Ireland remains within the UK to this day and why Irish republicans are still peeved by it. In the 1960s the Troubles started, with the republicans yet again attempting to extricate Northern Ireland from the UK and merge it with the Republic of Ireland - a 32-county Republic. This conflict was ended in 1998 with the passing of the Good Friday Agreement. One of the terms of the agreement was that the Republic of Ireland relinquish its claim to Northern Ireland. In two referendums held on 22nd May 1998, the Agreement was approved by voters across the island of Ireland.
The Highland clearances and the potato family populated pioneer Upper Canada. It wasn't their intention but the British founded a not very English country on the northern half of North America.
Although the Highland Clearances were perpetrated by Scotttish landowners. Nothing to do with the English.