Carbon offsetting went out of fashion after a huge outcry against it, based on, from what I can work out a) many of the schemes people were supporting turning out to be at best not delivering on their claims and at worst fraudulent b) people wanting to have a go at the nasty airlines, saying they were being sanctimonious / unreasonable suggesting that their passengers should give money c) a view that people should just stop flying rather than appease their conscience by paying some money to charity.
Well, it's still a thing, and better governed now, with a gold standard for the offset projects and more transparency.
This article from the common wanderer has loads of great detail all about it, but if you want to know the conclusion I came to after reading it and a few others, I'm now going to offset my flight carbon emissions by giving to atmosfair.de, a German carbon offsetting company with an industry leading carbon calculator and all projects meeting the Gold Standard. So, maybe this is about me appeasing my conscience, but the reality is I'm not going to stop flying and I figure doing something is better than doing nothing.