It's also not quite right. If you're burning wood thoroughly for power you get pure ash, which is just carbon neutral. You get charcoal in campfires because they're inefficient, and even then it's mostly ash. Carbon neutral is still better than fossil fuels, though!
I think the most discouraging about this for me is that even though I’ve seen countless headlines about climate change, I’ve never really bothered to be curious about it until now. Now I wish I knew how to tell this to other people without sounding like alarmist.
FWIW, it makes me feel better that there's people like you out there, who just didn't know the whole story yet, and who could still change and improve. Way too many people don't want to know inconvenient things.