Can you please support your statement with a reference to the source of that data?
https://ourworldindata.org/emissions-by-sector
All aviation is 1.9% … Private would be a vanishingly small amount of that.
That link does not have information on the contribution of private aviation. You are assuming it.
In this BBC article on What’s the climate impact of private jets you can read that
"Emissions per kilometre travelled [using an airplane] are known to be significantly worse than any other form of transport.
(…)
Private jets generally produce significantly more emissions per passenger than commercial flights."
Yes the BBC article is correct too. Just because CO2 emissions per km travelled are high doesn’t mean they’re statistically relevant in terms of total emissions. All aviation at 1.9% is basically not a meaningful amount of CO2 if you need a 50% reduction.
When weighted for KMs travelled a riding lawn mower is probably worse than a private jet by that logic.