The thing with that is that she has tried the "Do as I say, I am a Targaryen, the Unburnt, Mother of Dragons..." speech half a dozen times and it has never, ever worked. Instead, she has inspired loyalty either through her humanity or, in both cases of Dothraki, her supernatural powers.
If she'd approached her meeting with Jon like a leader instead of an entitled ruler, explained how she got there and what her plans for peace were then he probably would've responded better, just like everyone else she has encountered. But then I guess they wrote it like this to create some dramatic tension.
In mitigation it's also worth noting that Dany as a character is at a disadvantage because the audience knows Jon is right about the White Walkers and that by Dany's own "I am a Targaryen therefore the Iron Throne is mine" logic Jon has a better claim.

