I did wonder why Jon didn't make that case more strongly. He did say that, but she later said something about it being his "pride," to which he didn't reply. She obviously didn't understand what he had said earlier, but his silence only made it seem as if she was right. Jon never wanted to be "King of the North." He was trying to avoid it, so hardly anything to do with "pride." You would think that she would understand what it takes to be a leader rather than an imposed ruler, given that is also why she has such a large following.
Do the books say how the Dragons left Westeros? Did they all die of old age? Otherwise, where does it say that Dragons are invincible? I appreciate, that doesn't matter to the vast majority of soldiers; fighting an opponent with Dragons must seem like they are invincible in any case. However, if everyone thought Dragons were invincible then that weapon wouldn't have been built, and if Dany thought they were invincible she wouldn't have held back on using them for so long.