Questions in English are generally formed by inverting the subject and verb. Let's apply this to the following sentences:
You do not like peanut butter.
Do you not like peanut butter?
You don't like peanut butter.
Don't you like peanut butter?
Do not you like peanut butter?
isn't allowed, because you would have to treat "do not" as an inseparable combination in the inversion, and in standard modern English grammar, it's not; however, "don't" is.
If you ask: what is "Don't you like ..." a contraction for, I think the only reasonable answer is "Do you not like ...", but I don't believe that's the way it originated syntactically.
Google Ngrams shows that "Why do not you ..." was used in the past, but it also seems to show (not that it can be trusted in the 1600s) that "Why don't you ..." was used earlier, so I suspect that "Why do not you like" started as an uncontraction of "Why don't you like" ... people knew that they would say "Why don't you like", but they also knew that you shouldn't use contractions in formal writing, so they expanded it.