We gained our independence from Britain and now have different spellings for certain words. Why is this the case?

“The first answer is to blame Noah Webster, of Webster’s Dictionary fame. He believed it was important for America, a new and revolutionary nation, to assert its cultural independence from Britain through language. He wrote the first American spelling, grammar, and reading schoolbooks and the first American dictionary. He was also an ardent advocate of spelling reform, and thought words should be spelled more like they sound.”
For the rest of the explanation, visit Grammar Girl.