let's just cut down more trees :)?

My understanding is that synthesis of hydrocarbon fuels requires more energy than the fuel provides. It might make sense as a way of creating fuel for applications where only a fuel burning engine will meet the requirements, though bio-fuels are probably cheaper, and have other benefits. In most cases it would make more sense to use the energy required to synthesise fuel to directly power the transport, as in EVs, for example.
https://cleantechnica.com/2018/05/24/gas-from-grass-could-be-an-eco-friendly-bio-fuel/
https://cleantechnica.com/2018/05/23/the-pros-cons-of-bio-fuels/

It is only possible to turn CO2 into fuel by using about as much energy to run the process as will be contained in the fuel made. And then the fuel can only be burnt at about 30% thermal efficiency. So it only makes sense to supply the energy from renewables otherwise there is no point. And currently, everything green on our planet, from algae to oak trees are probably doing very nicely on all the extra CO2 currently available to them.

So unless we have surplus energy from renewable sources, we can burn fossil fuel thus creating more CO2 to produce energy to capture CO2. Its clear that perpetual motion machines don’t work, so with loss of energy on each cycle we generate more CO2 than we capture. It’s easy to say that we could only use renewable energy. But if the renewable energy could have been used somewhere else, then the fossil fuel used to create the energy used somewhere else creates more CO2. The net result is more CO2 either way. This solution is only viable if we are producing more renewable energy than we can use. And most countries are still a long way from this position.

Assuming the boffins are successful in removing all the CO2 from the atmosphere, how will we eat when no plants can grow without CO2? We have already driven up the price of corn by turning it into ethanol and burning it in our cars while poorer nations are scrambling to find food to feed their starving populations. In the 1950s, american "scientists" had a plan to cover snow with carbon to help it melt. We are like kids who find a rattlesnake and poke at it to see what it will do. Just keep poking and you will find out what it can do.

1. they suck in air to get the CO2 2. they go through all these processes to produce CO2. there must be a cheaper, easier way to get pure CO2. is CO2 heavier than nitrogen and Oxygen? a tall cylinder filled with air and baffles to prevent mixing might have the gases segregated? pull off the CO2 and flush the cylinder, start over? maybe i am just confused?

It's like we will do anything to keep burning oil. Plants remove CO2 from the atmosphere all the time and convert it to solid carbon forms. We just need to create an economic model (cap and trade) to sequester the carbon. For instance, turn switchgrass or waste wood into biochar (charcoal without aromatic tars) and return it to the soil or bury it. The last thing we need to do is go through an expensive process to remove CO2 from the air, only to burn it and put it right back into the atmosphere!

It would probably be more cost effective to reduce humidity and increase reflectivity in the dessert, where the bulk of thermal energy is processed.

Engineers should know how foolish this idea is.

I would have thought refrigeration would prove more effective in isolating carbon dioxide. However, what would be the point of producing a carbon based fuel from carbon dioxide. Apart from requiring as much, if not more energy to produce the fuel, as others have pointed out, what results when that fuel is burned? ... more carbon dioxide? What then does the process achieve?