The origins of the break between British and American spelling goes back to Noah Webster (Webster's Dictionary fame).
He changed the spelling because he thought it made things simpler...
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One facet of Webster's importance was his willingness to innovate when he thought innovation meant improvement. He was the first to document distinctively American vocabulary such as skunk, hickory, and chowder. Reasoning that many spelling conventions were artificial and needlessly confusing, he urged altering many words: musick to music, centre to center, and plough to plow, for example. (Other attempts at reform met with less acceptance, however, such as his support for modifying tongue to tung and women to wimmen—the latter of which he argued was "the old and true spelling" and the one that most accurately indicated its pronunciation.)
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It has also been suggested that due to the shortage of paper, newspaper barons decided this was the way to go as many of the spellings were shorter and therefore took up less space... I don't lend much creedence to this.