It's as simple as 'languages evolve over time'.
Accents become dialects, dialects become mutually unintelligible languages. The study of how languages evolve is called historical linguistics and is its fastest-growing component. By colonizing the Americas, the British created a pocket of society where citizens were geographically isolated from the rest of British society. Due to this separation of thousands of miles, the local language soon began evolving into its own accent, and was different than British English by 1776 (although both sound like a British accent to us today). Similar situations happened in Australia and Canada, which is why English speakers in those regions sound different than both American English speakers and British English speakers.