Why do anxiety and poor sleep make each other worse?

It runs in both directions, which is what makes it stubborn. Anxiety raises physiological arousal — heart rate, cortisol, mental rehearsal — which is precisely the state that prevents sleep onset. Then sleep deprivation measurably increases activity in the brain's threat-detection circuits and reduces the regulatory capacity that would normally dampen them, so the next day's anxiety is worse. Breaking the loop usually works better at the sleep end first: consistent wake time, light exposure in the morning, and getting out of bed if you have been awake more than twenty minutes rather than lying there rehearsing.