Whence came the construction, "Why do you think ...?" as in "Why do you think that American English is different from British English?"?

It’s idiomatic speaking in place of “why do you think the differences arose between American English and British English?” Notice that everyone understood the question.

Are you asking why people say “Why do you think…” versus “How do you know…” or “Why is…”, or what, exactly?

Idiomatic and colloquial speaking.

What are the differences between…?
Whence came the the differences between… ?
Why, do you think, are there differences between… ?
What makes you think there are differences between… ?

It’s just shorthand.