Why does Ahab seek revenge in Herman Melville's Moby Dick? What does Ahab offer the men if they help him kill Moby Dick?

As mentioned in the previously posted quotation, Ahab seeks "that intangible malignity" that he believes is embodied in the White Whale.  In a separate chapter (42), in fact, Melville considers the whiteness of the whale as symbolic of evil.  Even Ismael, the narrator, finds

It was the whiteness of the whale that above all things appalled me.....As for the white shark, the white gliding ghostliness of respose in that creature....This elusive quality....Now, in allusion to the white, silent stillness of deth in the shark, and the mild deadliness of his habits....Therefore, in his other moods, symbolise whatever grand or gracious thing he wll by whiteness, no man can deny that in its profundest idealised significance, it calls up a peculiar apparition to the soul.

It is this apparition of evil and mystery that Captain Ahab would not only avenge himself, but understand. Why is it white, Ishmael wonders, and why does it

appeal with such power to the soul, and more strange and far more portentous--why, as we have seen, it is at once the most meaning symbol of spiritual things, nay, the very veil of the Christians' Deity; and yet should be as it is, the intensify agent in things the most appalling to mankind. 

It is the "invisible spheres" that Ahab seeks to comprehend in his revenge against the whale.  When Starbuck tell him, "To be enraged with a dumb thing, Captain Ahab, seems blasphemous," Ahab replies,

Hark ye yet again--the little lower layer.  All visible objects, man, are but as pasteboard masks.  But in each event--in the living act, the doubted deed--there,, some unknown but still reasoning thing puts forth the moldings of its features from behind the unreasoning mask.  If man will strike, strike through the mask!  How can the prisoner reach outside except by thrusting through the wall?  To me, the White Whale is that wall, shoved near to me....He tasks me; he heaps me; I see in him outrageous strength, with an inscrutable malice sinewing it.  That inscrutable thing is chiefly what I hate; and be the White Whale agent...I will wreak that hate upon him....Truth hath no confines.

The preternatural White Whale wears the "pasteboard mask" that Captain Ahab is obsessed with striking through.  He would know what metaphysical meaning lies behind this creatures eye that cannot see before him, but only sideways from his head.  Revenge against him for his lost leg is a small part of what Ahab seeks; the Pequod's voyage is a metaphor for life and Ahab is man searching for meaning.