here is my question, why can’t we say: why did not you talk to me, but we can say why didn’t you talk to me?

Yoda talks this way.

When you study other languages (other than English) it helps you understand that there are parts of every language were the rules are played fast and loose. There are no 100% rules as to how the language is put together. As soon as rules are given the list of exceptions begin. This is the case with both the contractions in the question. You would not say, “why can not we say: why did not you talk to me?” The n’t denotes the negative of can and did. Like when someone says to me, “That’s the best answer I’ve ever read . . . NOT !!!

So in short, it’s not the same thing like jelly and jam aren’t the same or are not the same thing.

You can say “Why did not you talk to me?”, and people used to talk that way a hundred or so years ago. That’s why the contraction “didn’t” exists. It’s just considered old fashioned.

There’s no strict grammatical rule for where to place the negative in this case. It’s a matter of custom, and custom has shifted over time.

Okay, here goes:

The rule goes that in forming an interrogative, do not invert the negative “not” with the object unless it is attached as a contraction to the verb.

Saying “Why did not you talk to me” is both ungrammatical and non-idiomatic (meaning that it’s not a structure that’s used by native English speakers).

The first sentence correctly would be: why did you not talk to me, not why did not you talk to me.