Seems pretty clear to me? Flying is bad for the environment, spectacularly so. The alternative is not necessarily: flying without burning fuel. But rather: not flying.
And that isn't that big of a problem. We have many alternatives to flying, e.g. a high-speed rail system that has a 10x smaller impact. Of course you want to steer consumers towards that with incentives like these.
Earnings from these taxes don't just disappear in a black hole. They're redistributed. Perhaps to make train travel cheaper and more economically viable. Perhaps electric cars. Given the socioeconomic groups that most frequently use public transport vs air travel, this tax seems progressive, not regressive, if anything.
And that's only one alternative to flying: other forms of travel. Another is simply not travelling at all. There's a reason people don't choose to live 20 hours away from work, or choose to have a daily hobby in another country, or choose to visit friends across the world on a daily basis, because there's a cost to travel. A cost that is too high. And that's okay. Not all travel has to happen, not all travel is important enough to pay the cost.
May seem silly, but if we could teleport around the world for $1, with hypothetically insane costs to the environment, you'd have massive amounts of unnecessary travel. And the right response would be as a society that we could do without much of this unnecessary travel entirely, replace it with viable alternatives to proximity like a phonecall, a skype call, a text message, a picture etc. And we can do this by making it more expensive, and using that money to make low-impact alternatives (relatively) cheaper.
If you know that as a society we're destroying our environment and the current cost of doing so is too cheap, or the destruction is not factored in to the price, the most reasonable solution is to increase the cost.