Simply put, Ahab seeks revenge because the whale caused him to lose his leg.
Ahab does not see the whale as merely "a dumb brute...that...smote (him) from blindest instinct" Chapter 36). He sees in him rather "outrageous strength, with an inscrutable malice...(that) insulted (him)" (Chapter 36). He is obsessed, compelled to seek vengeance by an "innermost necessit(y) in (his) being" (Chapter 36), "damned in the midst of paradise" (Chapter 37), by "madness maddened" (Chapter 37). His heart is consumed by hatred and a deep-seated need to seek revenge, and he vows to pursue "that accursed white whale that...made a poor pegging lubber of (him)...round Good Hope, and round the Horn...and round perdition's flames before (he) give(s) him up" (Chapter 36).
Ahab seeks revenge for two reasons.
One he has been hunting Moby Dick for years and has not been able to kill him. He is frustrated by his inability to catch and kill Moby Dick. He personifies the whale into his mortal enemy.
And two, he lost his leg to Moby Dick so he is even more determined to kill him.
because moby dick ate his friend