Why is carbon dioxide produced in alcohol fermentation but not in lactic acid fermentation?
Glycolysis needs a steady supply of NAD+ to happen - this is the driver for the anaerobic oxidation to lactate and ethanol, although this is energetically much less favorable than the complete oxidation. But without oxygen there is no other way to keep the glycolysis active for at least some energy supply.

The difference is located in the enzymes available for the conversion of the pyruvate. This is the Lactate dehydrogenase in humans (and other mammals) and the Pyruvate decarboxylase in yeast. The first catalyzes the reaction from Pyruvate to Lactate, the second from Pyruvate to Acetaldehyde and CO2, the Acetaldehyde is subsequently converted to Ethanol. Only the second step produces NAD+.

See the illustration (from here) for further understanding:



The CO2 produced in this reaction does not occur due to oxidation, but is released from the decarboxylation of the Pyruvate. See the illustration below (from here): 



In the production of lactate no decarboxylation is happening which allows the backreaction from lactate to pyruvate once enough oxygen is present again.