For example: there are five major dialects of Hindi, some of which are mutually unintelligible -- yet few people call them separate languages. On the other hand, standard Hindi is mutually intelligible with Urdu -- they use different writing systems, but as spoken languages are roughly as close as American and British English -- yet they are considered different languages. Similarly, China has a vast diversity of mutually unintelligible languages -- or, rather, what outsiders call "languages", and what the Chinese government insists are merely dialects of a single language: "Chinese".

What's going on here? Max Weinreich's quip that "a language is a dialect with an army and a navy" seems to hit the mark. If Britain and America had not become allies in the late 19th century, then the ongoing antipathy between them would have required their speaking systems to be classified as "languages". But that would have been a political necessity, not a linguistic one.

As an aside -- as somebody who grew up in America and emigrated at age 31 to Britain -- I must say that the oft-cited differences in spelling and pronunciation are the least important areas of divergence. Much more significant (and confusing) are the idiomatic divergences. For example: in the UK, people commonly say "are you alright?" as a greeting, equivalent to the American "how do you do?" or "what's up?". But in American, "are you alright?" is an expression of serious concern -- something you might say to somebody walking around in a state of confusion with an apparent head injury. It was extremely disconcerting when people kept asking me this -- I thought I must be acting/looking really strange to provoke such continual concern!