I don't think that's a good analogy; IIRC organs (eg rabbit kidneys) have been successfully frozen and revived (good enough to implant), so it's more a matter of whether that can be extended to human brains (which, sure, may be more delicate) rather than being something inherently absurd.
Rabbit kidneys are much smaller than human brains.
The square-cube law is the main showstopper: you can remove heat form a thing at a rate proportional to its surface area, while its heat capacity is proportional to mass and thus to volume. Therefore, maximum attainable cooling speed decreases with size (if you try to cool any faster, youl'll just crack the surface).
Rabbit kidneys can be vitrified without using a toxic concentration of cryprotectants, moreover, IIUC the circulatory system of a kidney allows higher flow and pressure (a kidney is just a blood filter, after all), making cryoprotectant perfusion easier. Even then, cryopereservation isn't perfect: microscopic damage has been observed.
In the past, the Cryonics Institute has had a policy that said that they would not accept anyone who is not a member. This has changed. The policy now is that someone who has full legal authority over your body can sign you up after you die. It costs $36,250 to be frozen if you are not signed up, which is more expensive. They also will not do anything until you have been on dry ice for 2 weeks after they have been contacted, so not being a member is more risky.
This is very important news for anyone who is currently cryocrastinating. It means that you can drastically increase your chances of survival without filling out any forms. All you have to do is tell a loved one you want to be frozen upon death, and that you would like them to take responsibility for making sure this happens. This takes literally 30 seconds. Do it now!
This news might also be a reason to not sign up right away, if you think something better (like radical life extension or uploading) will come along in your lifetime. We should discuss this in the comments.
Edit: The general consensus of this discussion is that this is a really bad reason not to sign up for cryonics.