CO2 builds up during fermentation... as a beer brewer you know this. But some CO2 stays in solution at any temperature and pressure. Not enough to be fizzy, and to give good beer head, but enough to mess with the yeast and whatnot.
The more vigorous the fermentation, the more likely some backpressure from the airlock forced CO2 into solution -- i.e., carbonated your wine.
Stirring will change the pressure in the wine, with the pressure waves giving the gaseous solution enough energy to form bubbles and release the CO2. Did you notice a fine froth when you stirred? That was CO2, as you can verify yourself by trying to breathe it (not recommended).
Degassing is helpful for the yeast, I've been told, but you only want to do it if you are reasonably sure you are not introducing oxygen, i.e., you've been using your K-meta or campden or whatever brand/type/variety of metabisulfite you use.
So, to wrap up:
- oxidation turns wine brown and prevents long term storage
- metabisulfite "crowds out" oxygen, making wine less vulnerable
- a fully fermented wine and oxygen are NOT FRIENDS
- all fermented beverages are to a small extent carbonated during fermentation
Read more of that wine site Yooper linked and you'll understand it all very well.