Why do Republicans hate Obama
Republicans, for the most part, adhere blindly to conservative dogma; in 2008 a vast majority of Americans rejected conservative dogma and in essence told republicans and conservatives they were wrong.
Rightist ideologues
hate being told they are wrong.
Obama thus personified that rejection, and became the focus of republican hate.
Republicans also perceive the WH as their birthright; as authoritarians conservatives flourish in the venue of the Imperial Presidency, where executive orders can be issued and signing statements made absent consensus or compromise.
Last, Obama represents to conservatives a changing America, an acceptance of diversity that authoritarian conservatives despise.