They do not like each other for many reasons. Nadal doesn't like Kyrgios' attitude and behavior toward the game he respects and loves BUT more than anything, Rafa does NOT take kindly to people calling him out on on some of his tactics and getting favorable treatment from chair umpires. Most notably the time he takes to get ready to return a serve when the server is clearly ready. He's talked about Rafa's injuries to stifle the momentum of players in the past, and then turns around and is completely fine once he gets to see the trainer. Nobody stands up to Rafa in his mind, let alone a punk like Nick Kyrgios.
I need to look at Friday's schedule right now to make sure I am available to follow/watch that match!