From an early age, Irulan's father Shaddam IV expected her to become Empress after his death, or at the very least to wed a political ally and retain House Corrino's hegemony over the Imperium. The Bene Gesserit also saw potential in the girl, and gave her sufficient training so that they could exploit her at some point in the future, were she to find herself in a position of power.
However, despite the expectations of others, Irulan remained only an average Bene Gesserit adept, and retained a strong sense of personal identity and ambition: qualities that caused tension between herself and her equally strong-minded father. Lady Jessica mused that Irulan was too proud to progress very far with her Bene Gesserit training.
Me, after eating a fist full of blood pressure pills and resisting the primal urge to DUNE POST: