Blizzard cleanup is non-rivalrous (we can both simultaneously enjoy a snow free street) and non-excludible (if I pay to have the street cleaned, I can't tell you not to walk on it).
Diabetes treatment is rivalrous (insulin goes into your vein or mine, not both) and excludible (if you don't pay for insulin, you don't get any).
Obviously blizzard cleanup affects everyone and so is public. Diabetes treatment is private because if you get diabetes it doesn't affect me. You just have bad genes or ate too much sugar, not my fault and I'm not suffering for it. Really though it doesn't affect me because I basically don't care about anyone that isn't friends or family. Why should I help take care of your problems? Use your own bootstraps. I'd rather save my money for me and my own.
Well, federal disaster funds are pretty commonly used to pay for things like blizzards and hurricanes. So, while I agree with you that no one specifically mentioned it, I can understand how it would be an issue if we were to really dig into the whole "disaster cleanup" issue further. It is also the case that politicians who call one disaster aid package "wasteful" are quick to call for aid when their own regions are hit, so there's that.
So don't take care of my blizzard. I'm sure almost everyone else in my town will agree to give money to a local government that takes care of it. Basically my philosophy is that only the individual matters. Society is for the weak, and it only makes sense when a collection of rational men decide that it doesn't infringe on individual ambition.
Diabetes treatment is rivalrous (insulin goes into your vein or mine, not both) and excludible (if you don't pay for insulin, you don't get any).