I always feel the talks of private jets are missing the point. (Besides, it's always the private jets of Al Gore and Bill Gates that are in question. People never ask about the private jets of BP execs.)
To simplify, let's assume that Bill Gates has a Boeing 747, which burns about 38 pounds of fuel per mile [1]. Distance between New York (JFK) and London (LHR) is 3,440 mile. For a round trip, double that, so we have about 261k pounds, or 118 ton of fuel. Applying jet fuel to CO2 conversion ratio of 3.16 [2], we get about 374 ton of CO2.
If Bill Gates takes this trip every day for a year, we get about 137,000 tons of CO2. Okay, that's a lot! However,
Mankind emitted about 35 billion ton of CO2 in 2020. That's about 66,000 tons per minute. So Bill Gates would have contributed about two minute's worth of global warming in a year.
That's still an extremely large amount for a single person, but the question we should ask is, did Bill Gates's action (such as advocating nuclear power) result in delaying global warming by two minutes? Not one year, not even a day, but just two minutes?
Alternatively, did he speed up mankind's preparation, again, by two minutes?
If the answer to either question is Yes, then I'd argue that it's worth the CO2 spent on it.
Now let's invert the question. What's the justification for people who say "Fuck global warming!" and hop on a trip to Hawaii? Collectively they sustain many more flights per year, and it's not like most of them are doing anything substantial to mitigate AGW.
[1] https://en.wikipedia.org/wiki/Fuel_economy_in_aircraft
[2] https://www.eesi.org/papers/view/fact-sheet-the-growth-in-gr...