as i understand above history (my reading here is admittedly sketchy), several century-long ottoman control of territory that became iraq operated via keeping shia/sunni/kurd areas largely separate while maintaining 'alliance' with sunni elements that performed various gov't functions in all 3 regions, ottoman-sunni relationship, in effect, granted measure of power to latter that neither shia nor kurds had...
brits decided to 'unite' three regions into nation-state called 'iraq' (i believe that british chose the name), created a 'monarchy', and attempted to foster natonalist identity, one problem in all this was that ottoman-era power structure was kept, meaning that sunni elements had favored social position, kurds apparently did better both economically and politically during monarchy years than did shia...
late '50s coup that overthrew monarchy was rhetorically 'pan-arab', lot of shia improved although religious differences still played themselves out in socio-political ways, pan-arab ideology pretty much excluded kurds, one result was growth in kurdish 'nationalism'...
late 60s baathist coup led to iraqi gov't granting kurds degree of autonomy and entry of kurds into national gov't cabinet positions, meanwhile sunni-shia relations began to deteriorate again...
saddam hussein consolidated political power amidst anxiety created by iranian revo, khomeini called hussein an atheist and urged overthrow of iraqi gov't, shia uprising occurred in several iraqi cities, iraqi gov't responded with arrests/executions of iraqi shia political leaders who were accused of collaborating with iran...
hussein publicly "called out" khomeini, urged arab minority in Iran to revolt, and began mobilizing iraqi army in state of emergency/readiness that culminated in decade-long war between two countries... mh