Is it possible to environmentally offset long-distance air travel?

I've found the following, from NASA climate scientist James Hansen. It's from a book he has authored (quoted here):

The public must be firm and unwavering in demanding ‘no offsets’, because this sort of monkey business is exactly the type of thing that politicians love and will try to keep. Offsets are like the indulgences that were sold by the church in the Middle Ages. People of means loved indulgences, because they could practice any hanky-panky or worse, then simply purchase an indulgence to avoid punishment for their sins.

Bishops loved them too, because they brought in lots of moola. Anybody who argues for offsets today is either a sinner who wants to pretend he or she has done adequate penance or a bishop collecting moola.

My interpretation is that he is of the view that offsetting does not work, since people will continue their (carbon-polluting) business as usual, and the problem of global warming is left inadequately addressed.

Edit: I am drawn to this post recently by a comment under the question, so I will update this answer to a resource I found last year. This booklet expands on the claim that all of us, including travellers, must reject carbon-offsetting if carbon output is seriously to be challenged.

For what it's worth, I decided last year not to take the flight from the UK to Indonesia. I went to Scotland instead, by train.

Air travel burns fossil fuel, and therefore carbon that used to be buried deep under our planet's surface for millions of years ends up in the atmosphere as CO2. This is generally considered a bad thing because changing the long term global concentration of CO2 in the air changes the global climate.

You are basically asking "are commonly offered carbon offset schemes an effective way to reverse this effect of air travel", and I feel that is a question for the Skeptics stack exchange, as it needs thorough scientific consideration.

But you asked here, so that allows me to give my opinion that it's not, for two reasons:

One, the carbon was buried deep under the surface as part of our planet's long carbon cycle; a process that takes millions of years. Changes to it can't be fixed by planting extra trees, as the carbon that trees fix by growing and then release by dying and decomposing is part of the short carbon cycle. Even if the trees are replanted after dying, what's a realistic lifetime of a forest planted with your carbon offsetting money? A thousand years seems optimistic, and storing carbon for a thousand years does not offset releasing carbon that would have been stored for millions.

Second, if you hadn't flown, the oil would have been pumped up anyway. Oil is an incredibly useful substance and people are bidding on an open market for the right to burn it up (or make things with it that will eventually be burnt up). Unless countries with oil reserves get strong laws that forbid pumping up oil, all oil that can be pumped up using less total energy than it will generate by burning will be pumped up. Flying less just means that others get to burn it for a fractionally lower price.

TL,DR: Planting trees is a fine thing, but doesn't offset burning fossil fuel. If we want to stop global warming, we must make laws that forbid getting fossil fuel out of the ground.

In a first-order approximation, it definitely is technically possible to offset carbon emissions. There's very little debate about that. Both schemes to increase carbon capture (primarily tree planting) as well as schemes to decrease carbon emissions elsewhere (e.g. solar ovens for developing countries, eliminates wood ovens) work.

The two problems are however second-order effects and non-carbon pollution. If you have a forest planted, what use would have been made of the area otherwise? What about freshwater consumption? And even if you offset carbon, planes will still produce nitrous oxides high in the atmosphere.

The water vapor issue isn't that big a deal. Sure, the exhausts cause high-level clouds, but that's a short-term issue. Water in the atmosphere is in a quite stable balance, with rain removing excess water quite efficiently.

My opinion is that, indeed, non-essential travel should be cut out entirely. I agree that there is probably not enough "carbon offsets" for everyone, so on a global scale, the offset scheme is unsustainable. However, let me offer another important thing to consider: the impact you will have on people surrounding you. Refraining from flying sends out a much more powerful message than sending out money to some abstract organization.

People are naturally gregarious: the bar for what is considered "normal" is set by other people's behavior. So even if you do not think of yourself as a political activist, simply casually mentioning that you refrained from flying somewhere for ecological reasons will get people to think (while, on the contrary, describing to people the wonderful vacation you just had in Bali will encourage them to travel themselves). If someone hears this from several friends and acquaintances, he or she will start to feel a fairly intense pressure to follow them. (I am assuming that the person who knows about global warming, is not actively hostile to the idea that it is a real and grave threat, but lacks the motivation to actually change their lifestyle accordingly. Not everyone falls in this category but a lot of people do.)