The point is, Dany, since Vicerys died, has been presented as the de-facto winner in Westeros and everyone has been kissing her ass from Varys to Tyrion to Selmy and the ones who didn't, have died.
She wants dragons? She gets them. Wants an army? Gets it. An armada, she gets it. Whatever she doesn't have, she can just threaten/burn people to get it.
How can people like her is beyond me. The only character development she had was in season 1 / AGoT. As soon as the eggs hatched she became aggressively arrogant and simplistic in her world view and she's still the same ever since. Probably worse.
Renly's claim to the throne was awful, but Dany's even worse. At least he reasoned that he was very well liked, and he thought he was a decent human being. Dany's father was the worst King in Westeros and not a single reasonable human being would disagree with that he had to be killed. Hence, the rebellion and a new king. Dany's claim is based upon the delusion that her father was unjustly killed.
Taking into consideration the fact that her entire reason for her conquests is this silly claim, being brainwashed into her by her brother among others, she's nothing more that a delusional, philosophically bankrupt brat.
She wouldn't win a single argument without the whole ''i'm the mother of dragons, i have three of them so agree with me or burn'' thing she has going.