>means you can actually live at entirely carbon zero
That's not enough. You need to also do something to offset the carbon dioxide that went into manufacturing everything and the transportation for it. Make sure you plant a few hundred trees if you want to be at carbon zero. You also need to plant trees to replace the wood you burn. And you need to offset the CO2 from process of making any food you bring in as well. Otherwise it's an unjustified feel-good exercise to claim you are living at carbon zero.
Calling out blatantly incorrect statements is not letting perfect be the enemy of the good. Electricity side effects is such a small percentage of the CO2 from a single person that neutralizing it and claiming carbon zero is ridiculous.
It takes decades for those trees to grow to firewood size. In the meantime there will be carbon "in flight". Since the trees will be cut down and burned again, effectively replanting only reduces emissions by some fraction, dependent on the growth time. Burning wood, especially at your cabin, has a high emission rate, so an electric stove might be better, and fairly certainly is if powered by a solar panel.
Cut the trees down, make paper out of it, print government regulations and statistics and reports on it, store these in a vault permanently. You have a carbon sink.
It's a bit more complicated than that. The original source for the carbon that humans emit is the atmosphere itself, so overall humans are carbon neutral. And since a human body itself contains carbon, until it has completely decomposed the body itself is carbon negative.
trees have a lifecycle, and for the time the tree was a live, it was sequestering carbon from the atmosphere. firewood needn't come from a living tree. and cutting some down can leave room and nutrients for others to grow.
That's not enough. You need to also do something to offset the carbon dioxide that went into manufacturing everything and the transportation for it. Make sure you plant a few hundred trees if you want to be at carbon zero. You also need to plant trees to replace the wood you burn. And you need to offset the CO2 from process of making any food you bring in as well. Otherwise it's an unjustified feel-good exercise to claim you are living at carbon zero.