In Moby Dick, what are Starbuck's misgivings about Ahab's pursuit of the great white whale?
In "Moby Dick" Starbuck realizes that the hatred which Ahab harbors for the white whale is preternatural, not merely vengeance for the loss of his leg. For, Ahab perceives the great whale as possessing characteristics beyond its apparent nature. Starbuck cries,
Vengence on a dumb brute!...that simply smote thee from blindes instinct! Madness! To be enraged with a dumb thing, Captain Ahab, seems blasphemous
Having heard this, Ahab replies, addressing the entire crew,
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 undoubted deed--there, some unknown but still reasoning thing puts forth the moldings of it features from behind the unreasoning mask. If man will strike, strike though the mask!
In the white whale Ahab see "outrageous strength, with an inscrutable malice sinewing it." In short, Ahab endows Moby Dick with these preternatural powers and is driven to capture him in order to "break through the mask" and understand what lies beneath. Ahab is obsessed with the "inscrutable" whale and must kill it; he must know it.
Realizing the madness of Ahab, Starbuck murmurs, "God keep me!--keep us all!"
The answer above is important and marks a pivotal point in the novel, as Ahab shares some of his "reasoning" behind wanting to kill Moby Dick. Ahab's idea that the whale is evil emerges after Starbuck, an upright, honest, and straightforward kind of person, has articulated a rational and humane point of view that the whale is just a brute beast that acts from instinct and doesn't know what it does. However, Starbuck has another misgiving, which he also expresses to his captain.
Starbuck worries that Ahab is sacrificing the profitability of their voyage to revenge. Starbuck sees that Ahab has turned their business venture into a quest for vengeance against a single whale and questions how many dollars of return the pursuit of Moby Dick will bring, implying it is a waste. The men are out after any whale for the oil, so why go after this particular whale, who is especially dangerous and also hard to find? Why not just take any of the other whales that are available? The men have already killed some whales, but to Starbuck, pursuit of Moby Dick is still a foolish risk. This argument has some weight with Ahab, who wants to keep up appearances--but ultimately not enough to stop the madness.