Thing is, this claim is contradicted several times in the book:
The enmity between Queen Alicent and Princess Rhaenyra was passed on to their sons, and the queen’s three boys, the Princes Aegon, Aemond, and Daeron, grew to be bitter rivals of their Velaryon nephews, resentful of them for having stolen what they regarded as their birthright: the Iron Throne itself.
So Aegon is said to be resentful of Rhaenyra's boys for stealing what he regards as his birthright, but suddenly, when the usurpation comes, he magically regards the throne as Rhaenyra's birthright and is totally fine with it passing to her and her sons by extension?
He's supposedly reluctant to take the crown, and yet also impatient to be King:
Prince Aegon had grown weary of secrecy. “Am I a king or no?” he demanded of his mother. “If I am king, then crown me."
F&B: The Dying of the Dragons
And most importantly, he doesn't hesitate to immediately demand Rhaenyra's head when he hears of her coronation.
“My half-sister and my uncle are guilty of high treason,” the young king declared. “I want them attainted, I want them arrested, and I want them dead.”
F&B: The Dying of the Dragons
Meanwhile, Rhaenyra immediately offers pardons to her half-siblings and places the blame for the usurpation on Alicent and Otto.
Her first act as queen was to declare Ser Otto Hightower and Queen Alicent traitors and rebels. “As for my half-brothers and my sweet sister, Helaena,” she announced, “they have been led astray by the counsel of evil men. Let them come to Dragonstone, bend the knee, and ask my forgiveness, and I shall gladly spare their lives and take them back into my heart, for they are of my own blood, and no man or woman is as accursed as the kinslayer.”
F&B: The Dying of the Dragons
Like it shouldn't even be that hard to believe Aegon wanted this. He's grown up in a culture where sons are always valued over daughters and has heard time and time again he should inherit form his Mother's side and a good chunk of her supporters. And now, he finds himself second to a woman and what he perceives as baseborns. That's like the perfect recipe for aggrieved entitlement.
