I dont understand the difference between shia and sunni islam?

I know that shias beleive that the sucessor after Prophet Muhammad (صلى الله عليه وسلم) should have been Ali (R.A.) instead of the three caliphs who took over after him. but i dont understand why its a big deal. it was what it was, right? why do they take so much offense? and who appointed the caliphs?
Update: i feel like you guys are giving biased answers based on whether you're sunni or shia. give me some unbiased facts.
Update 2: the last one was good.
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