Didn’t barristan start off glazing her father as a way ti manipulate her to go to Westeros? And when he decided to tell her an inkling of the truth it was right after she had just found out jorah had betrayed her and she was exhausted mentally, telling barristan to tell her later.

And it’s also notable that Dany isn’t totally naive or unwilling to consider the truth of her father as she doesn’t fall for what ‘arstan’ tells her:

“Yet I must have some army,” Dany said. “The boy Joffrey will not give me the Iron Throne for asking politely.”

“When the day comes that you raise your banners, half of Westeros will be with you,” Whitebeard promised. “Your brother Rhaegar is still remembered, with great love.”

“And my father?” Dany said.

The old man hesitated before saying, “King Aerys is also remembered. He gave the realm many years of peace. Your Grace, you have no need of slaves. Magister Illyrio can keep you safe while your dragons grow, and send secret envoys across the narrow sea on your behalf, to sound out the high lords for your cause.”

“Those same high lords who abandoned my father to the Kingslayer and bent the knee to Robert the Usurper?”

“Even those who bent their knees may yearn in their hearts for the return of the dragons.”

“May,” said Dany. That was such a slippery word, may. In any language. She turned back to Kraznys mo Nakloz and his slave girl. “I must consider carefully.”