The Cthaeh lied to Kvothe. It said that Kvothe would never ask Denna to leave Master Ash, and if he did she would never agree.
But spurned by that comment Kvothe did ask her, and she did agree to leave him. They made plans to meet in a small village a span later, giving her time to collect her things. Kvothe didn’t truly understand Master Ash, and Denna didn’t either. What Master Ash has, Master Ash keeps. If he cannot keep what is his, no one else can have it either.
Kote isn’t Kvothe in hiding, Kote is Kvothe waiting. Terrified to leave and miss her, never knowing what happened. Kept from helping the world or exacting revenge by bonds stronger than iron.
The Cthaeh sees all futures, and sets us down the worst one.