Doesn't the net CO2 in the air increase? So you harvest CO2 to into fuel. That fuel is burned and the CO2 is released back into the air. So net difference is zero. But to harvest the CO2 you needed to generate a high amount of heat. That's extra CO2. So net CO2 is more. It depends on the cost of harvesting that CO2.
You can use Solar and other renewable energy to power the conversion process. Progress is still progress. I would much rather to pay more for net zero carbon fuel, then not do anything.
Whether something is net zero depends on what you are adding it to; it's not inherent in that thing.
It's like, if you have a pile of blue things, then the pile is also blue. But other characteristics do not work that way. If you have a pile of things that each weigh 1 lb, then the pile does not weigh 1 lb.