I'm not sure why you are lumping those two modes of transport together. According to one estimate, "a passenger traveling in a private aircraft emits ... between 75 and 250 times the CO2 of a comparable high-speed rail journey."[0]
You're right, though, that private jets are an easy target for a carbon tax, and I don't know of any climate activists arguing that private jets should be exempt from one.
Perhaps the reason it is not high on people's lists of things to fix, though, is that "the aviation industry only contributes around 2% of global CO2 emissions, with private air travel representing an even smaller fraction." (according to the European Business Aviation Association).[0]
[0] https://www.dw.com/en/should-private-jets-be-banned-to-spare...