I was confused as well. Alcohol dehydrogenase is important for all herbivores and omnivores. Mammals have evolved to have this enzyme ready so that when wondering around we can eat any fruit and not have to worry about dying from ethanol poisoning if the fruit is a bit old and fermented. Humans take advantage of the fact that we do not have enough alcohol dehydrogenase to quickly clear the amount of ethanol we drink in a beer, thus we fell the intoxicating effects.
The enzyme Alcohol Dehydrogenase breaks down alcohol into less toxic compounds that are eliminated from the body. This works great for ethanol.
However, when ethylene glycol (Antifreeze) is ingested, the body tries to detoxify it by using Alcohol Dehydrogenase. Unfortunately, this leads to an increase in toxic compounds (the opposite of what happens with ethanol). Antifreeze, by its self is not very toxic. But when it get broken down, it becomes extremely toxic. It turns your brain to mush, your blood to acid, and your kidneys to stone. Once it gets broken down, your cat is as good as dead.
The treatment for antifreeze poisoning is
preventing this breakdown. When I have a cat that ate antifreeze, I instruct the owners to buy a bottle of Vodka and bring it in with them. Then, I put the cat in an alcohol-induced coma by giving the vodka in an IV drip. This is very dangerous, but it is the only chance to save the cat.
When the cat gets alcohol, then body stops trying to break down the antifreeze and tries to breakdown the alcohol instead. The antifreeze is then eliminated, unchanged, from the body.
So, now you only have to deal with a comatose cat - which is bad. This is the lesser of 2 evils. Certain death from the antifreeze versus probable death - from alcohol poisoning. If you want any change of an alive cat, that is the only option.
Cats can breakdown alcohol like every other mammal can. But, their small size leads to easier overdosing. This can cause neurologic, intestinal, metabolic, liver, cardiovascular, and low blood sugar.