Wood or other biomass-fueled fires are CO2-neutral, but do cause particulate pollution. There have been a number of efforts to develop clean-burning wood stoves for developing countries to combat that problem.
Okay, I'll bite. How does burning wood not result in a net increase in CO2? Are you assuming that for every cord of wood burnt, that someone is simultaneously planing and growing a cord's worth of tree (which, of course, pulls carbon out of the air?)
That's a pretty big assumption.
Carbon embodied in coal, oil, and gas was last part of the biosphere hundreds of millions of years ago. And that's precisely the problem: humans have re-introduced, mostly in the past 50 years (95% of all oil was burned since then, a large portion of coal and gas) carbon that was deposited over hundreds of millions of years. The biosphere portion of the carbon cycle (atmospheric uptake, oceans, plant growth) simply cannot keep up.
Yes, if you were to burn all forests at once, you'd run up CO2 a bit. That is, however, a pretty self-limiting prospect.
At one point, there was some n amount of CO2 in the air.
A tree was planted. Through a few biological cycles, CO2 is exchanged and stored as various sugars within the wood.
Burning the wood releases the CO2 back into the air.
This is a net zero process.