I doubt there are any direct subsidies to private jets.
However, the poster could have been talking about subsidies to private aviation. Yes, private aircraft pay landing fees etc. at the airports that they use. However – not all small airports make enough in landing fees to pay for their existence. Therefore, a lot of airports would go under without federal subsidy. Therefore, the private jets would have a lot fewer places to land. Not being able to land in as many places, and having to use less convenient airports instead – would take a lot of value out of owning a private jet.
That being said – do I support subsidizing private aviation via small airports? Yep.