Edit: To put numbers on it, each American emits 16,500 kg of CO2 per year, 2400 gallons of jet fuel emits 21,360 kg of CO2. So it's more like one American's emissions in a year.
That still seems horrible to me.
IMO, the main advantage of flying private is the convenience of getting to bypass the whole airport experience. At least on the small business jet flights I've been on, the actual flight is less comfortable. The interior has nicer decor, but it's also cramped and noisy. And then, yeah, you have to eat nothing but rice and lentils for the next two months to try and offset the carbon.
But in this case you have to compare U.S. domestic business class to private travel, where I would argue the in-flight experience is still better on a small private jet. (I guess unless you are sharing a jet like the services you mention)
If you're talking about first class, as this article is, then you're talking about long international flights. The cramped and noisy private jets won't take you non-stop from NYC to Tokyo, for example.
Edit: I neglected to convert for the average American's carbon footprint (about 16500 kg CO2/yr as stated elsewhere in the thread). Each of the 6 Citation pax emits (21 lbs CO2/gal * 1000 lbs / 6.7 lbs/gal) = ~3.1k lbs CO2, or ~1400 kg CO2 during the flight—about 1/10 of the average yearly footprint.
https://www.thisisinsider.com/fake-private-jet-interior-insi...