Coil may have lost his handle on a lot of things right now, has no idea what to think about the revelation that had just been made, and couldn't explain why he's currently panicking so badly over it... but there is one thing that he is in fact sure about.

When Carl asks if he should leave, Coil turns back to face him--teary-eyed because of course that always has to be part of his panic on top the rest of the humiliation--and shakes his head. Emphatically.

He doesn't want him to go anywhere.

And being forced to think long enough to answer a question helps interrupt the runaway train of anxiety. He's able to drag in a longer breath and drag the back of a shaking hand across his eye.