In addition burning biofuels like wood briquettes and wood pellets at home release horrific amounts of carbon monoxide and other small particulate from incomplete combustion. Stuff that does horrific things to local air quality, we'll see the return of impenetrable smog to our cities, and health warnings telling asthmatics not to go outside for risk of dying due to inhaling all the nasties.
Insulation is really the most important thing to reduce a building energy consumption (some buildings are even built with zero heating: https://en.wikipedia.org/wiki/Zero_heating_building), along with air-tightness and heat_recovery_ventilation.
See also: clearing land (including fragile desert ecosystems!) for solar farms vs residential/urban solar, biofuels in general, subsidizing EVs which encourage poor land use and sprawl vs legalizing denser housing and building better public transport, etc etc etc.
When you burn wood, the CO2 released into the atmosphere gets re-absorbed by the next batch of trees that you're gonna burn next year. The overall process can be carbon-neutral, neither increasing nor decreasing the total amount of carbon in the atmosphere.
Once gas comes out of the ground, it's guaranteed to get into the atmosphere one way or another, and it's never going back down in there.
Fuel wood comes from farmed forests that re-plant every tree they take down to recycle the forest every 25-30 years.
Deforestation is bad, but it doesn't happen because people want timber. Deforestation happens because people want to use that land for something other than growing trees, the most common reason being to make room for cattle pasture.
If you want to save the trees, don't stop burning wood, almost all wood products available today come from sustainably farmed managed forests. If you want to save the trees, stop eating beef. Also palm oil.