But, the blood system in warm blooded animals like humans already have less than 1mm contact with all tissue (so that they can get oxygen).

And they can freeze small animals (like hamsters) and unfreeze them and they live...

So what exactly prevents us from hooking the circulatory system to a liquid nitrogen pump and freezing the body that way?

Well, one issue I can think of is that unfreezing would be much more difficult, you'd need some advanced microwave that can focus the waves in a grid of 1mm points too. (The microwave was literally invented to reanimate frozen hamsters but they are small...)

Another issue is that it's just too finicky when freezing because droplets of blood will come into contact with the freezing liquid and freeze immediately and block the blood vessels.

One possible solution I have in mind is that they could use multiple liquids in quick succession like this: quickly and fully flush the blood out with the help of some cold liquid that won't freeze blood and that has a very low freezing point, monitor blood being flushed out, then once done, flush with a freezing liquid with a temperature above the freezing point of the first liquid but below or at your target body freezing temperature.

Short counter-argument:

When infected with rabies, a human will flinch and try to move away from water or push it away as soon as the water is close to their mouth! So no, human behavior too can be "automatic" or "manipulated".

(You can find a real video on wikipedia if you wanna see the behavior for yourself...)

Any sources? Like, was there ever a beaver adopted by a human at birth and never saw dam building and started building a dam?