I’m sorry it took me so long to look at this. I needed to do a bit of research. I am not entirely sure whether by “power-sharing” you mean the concept or the specific institutions of the Executive set up in 1973 so I’ll deal with both. Michael Kerr has argued that the idea of power-sharing was not the central issue for most unionists but I’ll address this when I look at the executive. For those unionists who did object to it we tend to see three main problems.

1. Democracy: unionists, such as William Craig, complained that British tradition was that the majority should rule and that it was anti-democratic for this to be changed for Northern Ireland. They simply denied the existence of discrimination under Stormont. The fact that the negotiation process was long and drawn out made it look more like a shady back room deal.
2. Nationalist disloyalty: the idea that politicians who opposed the existence of Northern Ireland and wanted a united Ireland should be included in government appalled many. They believed that there was little difference between constitutional and violent nationalism and that power-sharing was just a first step towards unification. The SDLP reinforced this view by selling the executive to their voters as a stepping stone to unity and by holding high profile meetings with the Irish government.
3. Zero-sum politics. A perennial problem in Northern Ireland has been that the communities see any gain for the other as a loss for themselves. The 1973 arrangement saw nationalists gain power-sharing but unionists only gained a reduced level of self-government in return. It was assumed that this meant unionists had been the ‘losers’. As regards the executive, its biggest problem was not power-sharing but its link to the Sunningdale process. Michael Kerr argues that power-sharing was not as unpopular among the unionist public as it was among the elite. However, the Sunningdale process promised a Council of Ireland with real powers. This was politically toxic. The council of Ireland is far more prevalent in unionist propaganda than is power-sharing. Unfortunately neither the Irish nor the SDLP were willing to make concessions on this issue. Both were under political pressure and the Irish Government also had to uphold Articles 2 and 3 of the Irish constitution.
   The executive also suffered from the fact that violence actually worsened while it was in existence. Therefore it was seen as a side issue rather than a solution. Sources Loyalist Association of Workers (LAW). (1973) 'Surrender and Betrayal', LAW, Vol.2, No.49 Bloomfield, K. (1974). 'The Northern Ireland Executive: Some Retrospective Conclusions', (19 July 1974), (Constitutional Convention; Sunningdale), [PRONI Public Records CENT/1/3/24; 5 pages], [PDF; 917KB]. Belfast: PRONI. ... William Craig, The Future of Northern Ireland (n.d; 1972?) Dr Mary-Alice Clancy, Peace Without Consensus: Power Sharing Politics in Northern Ireland Paul Dixon, Eamonn O'Kane, Northern Ireland Since 1969 Eric P. Kaufmann, The Orange Order: A Contemporary Northern Irish History Michael Kerr, Imposing power-sharing: conflict and coexistence in Northern Ireland and Lebanon Allison McCulloch, Power-Sharing and Political Stability in Deeply Divided Societies