I suppose I should qualify that by saying I understand why nationalists in Northern Ireland would support their own parties instead of British ones (though many members of Labour - including newly minted leader Jeremy Corbyn - supported the nationalists). But why did unionists start their own political parties instead of supporting, say, the Tories? It's odd to see the major UK parties historically contesting seats in Wales and Scotland, but not Northern Ireland.
The evolution of a particular Northern Irish political party system predated the invention of the Northern Irish state. There were already parties focused on the issue of Home Rule and these were divided along nationalist/unionist lines prior to the First Home Rule Bill in 1886. For example, Isaac Butt had already created an several different Home Rule confederations in the 1870s before he was eclipsed by Charles Stewart Parnell. The Unionists formed their first specifically Irish party, The Irish Loyal and Patriotic Union, in 1885. This particular party formed the bedrock for a number of later political parties, most notably the Ulster Unionist Council (UUC) and the Irish Unionist Alliance, which focused upon Unionism in the south. The mushrooming process of these political accelerated in the early twentieth century as the Third Home Rule Bill loomed on the horizon. After the partition and establishment of Northern Ireland, these political parties became more permanent parts of the Northern Irish electoral landscape.
As to why Unionists did not vote for established political parties, a number of Unionists feared that neither the Liberals nor the Conservatives/Tories cared much about the Irish question. Due to a divide in the Liberal party on this issue, Unionist of a Liberal bent had formed the Liberal Unionist Association. But this party only survived a few years and lacked the staying power of its more conservative counterparts. On the surface, the late-nineteenth and early twentieth-century Conservatives/Tories seemed like a natural ally for unionists. The Primrose League had courted Irish unionists and opened branches of their organization in the 1880s and 90s. Similarly, between 1910-14, the Conservatives took a fairly radical approach to Unionism with some Tory money funneled towards Unionist paramilitary organizations, specifically, the Ulster Volunteer Force (UVF). However, this support was much more about the Conservative party trying to win back Unionist voters and stave off the double pressure of the Liberals and Labour on shrinking Conservative electoral base. Prior to this, the Conservatives had proven themselves to be an inconstant ally for Unionism. But these efforts to win favor among Unionists had shallow roots. They were often dependent upon local Unionist organizers for these efforts, and often these political figures had a dual allegiance, serving both in Unionist organizations and Conservative ones. These courting efforts never erased Unionists' general skepticism about the government and those who were a part of the existing system. In this context, Unionism would always trump any other political cause.
For nationalists, forming independent parties had an even deeper roots than it did with Unionists, dating back at least to Catholic Emancipation and one could argue even earlier depending on the definition of party. Like the Unionists, Home Rule galvanized this process of Nationalist political separatism and it accrued some rather notable results. By 1880, the Irish Home Rule Party had captured sixty seats in the general election, compared to twenty-three Conservatives and twenty Liberals elected for Ireland. The Home Rulers had some hopes for an alliance with Liberals or Labour, but they also recognized Home Rule was divisive for both parties. So in this case striking out on their own pushed Home Rule further along than if they had worked within the system. By 1905, these disparate nationalist parties had consolidated into an umbrella political party of Sinn Fein.
In short, Nationalists and Unionists shared a common distrust of the British government prior to Partition. The establishment of increasingly formal political organizations laid the foundations for both Nationalist and Unionist parties of the twentieth century. Sinn Fein and the Ulster Unionist Council would both eventually give birth to a myriad of political organizations. Major divisions of these political parties would take place in the 1920s and again during the 1970s with the rise of The Troubles. Irish politics became uniquely Irish during the invention of mass politics in the nineteenth century, long before the creation of Northern Ireland.
Sources
Bew, Paul. Ideology and the Irish Question: Ulster Unionism and Irish Nationalism, 1912-1916. Oxford: Clarendon Press, 1994.
Boyce, David George, and Alan O'Day. The Ulster Crisis: 1885-1921. Houndmills, Basingstoke, Hampshire, England: Palgrave Macmillan, 2006.
Buckland, Patrick. Irish Unionism, 1885-1923: A Documentary History. Belfast: H.M. Stationery Off, 1973.
Smith, Jeremy. The Tories and Ireland: Conservative Party Politics and the Home Rule Crisis, 1910-1914. Dublin: Irish Academic Press, 2000.