If you compare it to burning fossil fuels, we've been burning fossil fuels in large amounts for our power sources, for example, for many years and we're now able to get a large percentage of the air pollutants out of the air when we burn fossil fuels. Certainly the volume that we're producing still produces a lot of air pollution, but there's good technology for getting many of the air pollutants down, at least.
There's very little technology at the moment for reducing CO2, however, from fossil fuels. If you look at the technology that's available for burning biomass, it's at a much more primitive level. If you look at your own wood stove, even if it's an EPA-approved wood stove that greatly reduces emissions, the emissions that come out of those are still quite a bit higher than if you were burning an equivalent amount of coal in a well-stocked, fitted-out power plant.
One of the recommendations that have been considered for addressing climate change is using renewables, for example. Wood is a renewable resource. Its contribution to greenhouse gases is supposed to be equal. It sucks up as much CO2 when it grows as it emits when you burn it, or roughly equivalent. However, the problem with using that as a climate change solution is that it produces a lot of air pollution. So it would be a poor choice as a climate change solution because of its problems with air pollution.