I a word.

"My liver and kidneys work pretty well."

Also headaches, migraines, agitation can be caused by lower blood sugar and lower blood pressure than what you are used to.

I believe the idea is toxins do tend to get stored in fat, so when you are running on stored fat - you can release them. I can confirm you can have sudden ups and downs when fasting and I never experienced headaches until i started.

Your body is digesting food that remained in your intestines and also fat deposits. Toxins are in the fat and removing undigested food can have a liberating affect.