Sorry, it's just that these kinds of threads have a lot of people repeating things that aren't really all that correct. It creates an image of things that doesn't match reality that continue to persist in the collective conscience. Like how hibernation for bears isn't really "the bear sleeps all winter." Anyway, neither here nor there (I'm still not happy I lived 35 years of my life believing bears curled up in caves and take 3-month-long naps for winter. It's preposterous on its very face).

Solutions of alcohol and water are weird. If you had a solution of salt and water, you could boil 100% of the water out in one go and have 100% of the salt left over. With alcohol and water, you don't get that. You get a continuum of concentrations that changes over time, as the distillation progresses.

And there is more than one alcohol that you're dealing with, with different phase change temperatures for each. So it's a bit like homeopathy. At any particular point, you are dividing the batch into two sections, one that is increasing on the gradient of alcohol concentration and one that is decreasing. But each part of the batch will actually have some proportion of each chemical in it. All you can do is change the relative proportions and repeat until you've changed the ratios such that the one you don't want is negligible.

Water's freezing point is 0C, of course. Methanol's is, like, -97C. Ethanol's is around -115C. Something like that. So "the water freezes first". But it's not just water. It will be some proportion of all three, as well as trace other acetyl alcohols where the flavor comes from. It's just that more of it will be water than what you started. On the flip side, the ethanol freezes "last". But again, it will be a certain proportion of all three. So the "remaining, unfrozen liquid" increases in ABV over time. But the frozen liquid is not free of alcohol. And if we were trying to run a production distillery, we'd want to reprocess the frozen portion to extract the remaining aclohol from it as well.

It's an infinite series on which we're performing a manual, physical Taylor expansion approximation.

One of the nice things about boiling distillation is that it is the methanol with the lowest boiling point and the water with the highest. So, you can more easily bracket your product away from the beginning parts of the process to avoid the methanol. You can't really do that with freeze distillation, because the methanol is sitting in the middle between the water and ethanol in the phase change spectrum. Thankfully, it's impossible to make yourself go blind from in-good-faith home brewing and distilling. The amount of methanol you can produce will--at worst--give you a wicked hangover. But that's why more people don't do freeze distillation.