Even today's airline industry is unsustainable and can only continue to function because it's heavily subsidised.
Fossil fuel for airplanes is tax-free and cheaper than petrol, e.g. $3.31/gal w/o taxes in California [0] vs. $2.06/gal (average) for jet fuel [1].
Using atmospheric carbon to generate fuel is significantly more expensive than that as even just capturing the CO² costs more than the crude oil used for jet fuel [2].
The claim of "carbon neutral fuel" basically rests on super optimistic assumptions already. The cost can only be competitive if a world-wide carbon tax on the order of $200/metric ton is implemented, which is very unrealistic.
This is total insanity, why are we doing this