It was Alan's fault that Cane reacted so drastically. If only he didn't provoke him, he wouldn't have said those things out loud, reminded all of them about how King Aeon succeeded the throne, even though he was born to a mistress, the same as Alan.
The current crown prince was also born to a mistress and this didn't project the King and his favorite son in good light, who he stubbornly appointed as the Crown Prince, as it gave a feeling that King Aeon reflected himself so much in Alan.
As of now, the King was fuming mad upon the Crown Prince's slip and how clueless he was about his own predicament.