Today when someone tells you "thank you" the common reply is "no...thank you".
Now to explain what that means. You do an act of kindness for someone, maybe holding a door open, and that person tells you "thank you".
You reply, "no...thank you". In reality you told the person that thanked you for your kindness that you do not accept their thanks, you reject it, and you thank them back. But what for?
This happens all the time today, when a news anchor tosses a story to a field reporter after the story you hear, "thanks Ron". "No thank you for reporting that." Or at a bank the teller thanks you for using their bank, you reply, "no...thank you."
In all cases replying thank you to a thank you is a rude reply. You are in effect telling the person you totally reject their thanks and yours is better.
The proper reply to a "thank you" is "your welcome".