You probably know that medieval medicine relied on the idea that the body functions by balancing four humors, each produced by a major organ. The liver makes yellow bile (to make you choleric), the heart makes blood (to make you sanguine), and the spleen makes black bile (to make you melancholic), which leaves us with one more humor: phlegm.
What organ produces phlegm? you may ask.
Answer: the BRAIN!
Apparently, the brain grows throughout a person's life, which is problematic because it is constricted by the skull. What's to become of the excess brain matter??
Answer: Expel it through the nose!!!
...In case you didn't catch the implications of that momentous statement, I shall elaborate. This means that all the phlegm you blow out your nose or cough up when you're sick is actually brain matter that just didn't fit in your head any more. I.e., snot == brains. Yes.