I once drank a soda so fast that it was fizzing back up my throat. It isn't hard to chug. (If it wazn't fizzing up my throat, it sure felt like it. I kept having to swallow it back down.)

The process of carbonation creates carbonic acid, which when agitated, becomes C_O2 and H₂O. [So Carbonic acid is H₂CO₃]

Where else would all of that CO₂ come from?

The sugar, as well as carbonic acid is what eats your teeth [there's something else in coke too, which makes it stronger, but I can't remember]

Your teeth are full of OH bonds that are easily pulled off by acids, but that doesn't decay teeth. Acids simply remove an outer covering, which allows sugars to get in and lay a spot for bacteria. Most acids alone don't do anything to teeth. (As a side note, fluoride toothpaste works by removing the OH bonds and replacing them if F bonds, which are harder to pull off.)
And the acid your probably thinking of is Phosphoric acid, which removes rust, (by a similar mechanism that it removes OH's from teeth.) but that doesn't dig deep into teeth.

The best advice is to brush so bacteria doesn't start building up.

Actually bacteria doesn't dig directly into the teeth. They eat the suggar and convert it into acids by extracting its energy. Those acids make the pH drop and the low pH dissolves teeth.
I find funny that cavities are actually created by the bacteria crap.

Yeah, they're like humans! Destroying by waste.

Water existing creates carbonic acid. And you exhale CO2 (and, of course, whatever gasses were not absorbed by your lungs. )