Well, there's a heck of a lot artificial intelligence can't do yet, but in this post I'm going to give an example of a conversation that no computer program can have. There's no existing theory that explains how humans are capable of this either.
a: What is the capital of Spain?
a: Why did you say Madrid?
b: Because you asked what the capital of Spain is.
a: Why did you answer?
b: Because we're having a conversation.
a: How did you know the capital of Spain?
b: I looked it up on Google.
a: Why did you do that?
b: Because you wanted to know, and I didn't know already.
a: Why did you want to find the answer to my question?
b: Because I felt like it.
a: Why did you feel like it?
b: I like to be helpful.
a: Why do you like to be helpful?
b: It makes me feel good.
a: Why do you like to feel good?
And so forth. Humans can go on like this forever, explaining their feelings and notions in ever-increasing detail, as abstractly as necessary. We don't really know why we feel certain ways, but we can guess based on our history and experience and make ourselves understood to each other -- because our brains all work in the same general way. We may not be able to verbalize it all, but when someone says "you know what I mean", we do.
Computers don't. No computer program can explain its own workings to you. Why? Because you'd have to create code that did the explaining, and then you'd have to create code that explained that code, and so forth. The series of "why?" questions can go on uniquely forever. No one knows how we handle it, and no one knows how to make a computer do it.