Probably Isn't it a mistake of "こちらこそ"?

Usually we use こちらこそ、when the person that talked to you said something that you feel you should be the one saying so. We use こちらこそ、in situations like: ーいろいろありがとうございました。(Thank you very much for all) ーこちらこそ、ありがとうございました。(Thank YOU very much) (I am the one that should be thanking you) By the way こちらIs a polite way to say こっちwhich means here and こそis a word we use to put emphasis on what you are saying.

こちらこそ？　　不是こちりこそ