It's a question that Melville must dispense with sooner or later. We have to see the confrontation between Ahab and the white whale; that's the whole reason this novel exists. We also have to see Ahab's insanity long before that, so we know how doomed this trip is. The crew members know also. The fact that they know increases the drama; we watch helplessly as they struggle with and tame their misgivings. Still...Ahab is one man, and an old one (with an ivory leg, no less). How hard would it be to take him out? Melville answers the question via Starbuck's interior monologue in "The Musket." Starbuck, watching Ahab sleep in his hammock, has Ahab's musket in his hands. All he has to do is shoot--or failing that, take him prisoner. The latter would seem a fine alternative to out-and-out murder.
Ha! is he muttering in his sleep? Yes, just there,--in there, he's sleeping. Sleeping? aye, but still alive, and soon awake again. I can't withstand thee, then, old man. Not reasoning; not remonstrance; not entreaty wilt thou hearken to; all this thou scornest. Flat obedience to thy own flat commands, this is all thou breathest. Aye, and say'st the men have vow'd thy vow; say'st all of us are Ahabs. Great God forbid!-- But is there no other way? no lawful way?--Make him a prisoner to be taken home? What! hope to wrest this old man's living power from his own living hands? Only a fool would try it. Say he were pinioned even; knotted all over with ropes and hawsers; chained down to ring-bolts on this cabin floor; he would be more hideous than a caged tiger, then. I could not endure the sight; could not possibly fly his howlings; all comfort, sleep itself, inestimable reason would leave me on the long intolerable voyage. What, then, remains? The land is hundreds of leagues away, and locked Japan the nearest. I stand alone here upon an open sea, with two oceans and a whole continent between me and law.--Aye, aye, 'tis so.-- Is heaven a murderer when its lightning strikes a would-be murderer in his bed, tindering sheets and skin together?-- And would I be a murderer, then, if"--and slowly, stealthily, and half sideways looking, he placed the loaded musket's end against the door.
"On this level, Ahab's hammock swings within; his head this way. A touch, and Starbuck may survive to hug his wife and child again.-- Oh Mary! Mary!--boy! boy! boy!--But if I wake thee not to death, old man, who can tell to what unsounded deeps Starbuck's body this day week may sink, with all the crew! Great God, where art Thou? Shall I? shall I?--The wind has gone down and shifted, sir; the fore and main topsails are reefed and set! she heads her course."
"Stern all! Oh Moby Dick, I clutch thy heart at last!"
Such were the sounds that now came hurtling from out the old man's tormented sleep, as if Starbuck's voice had caused the long dumb dream to speak.
The yet levelled musket shook like a drunkard's arm against the panel; Starbuck seemed wrestling with an angel, but turning from the door, he placed the death-tube in its rack, and left the place.
"He's too sound asleep, Mr. Stubb; go thou down, and wake him, and tell him. I must see to the deck here. Thou know'st what to say."
In the end, Starbuck doesn't have it in him to shoot Ahab. That makes sense; we've seen that Starbuck is the least bloodthirsty of the whale hunters. But he also can't take Ahab captive because he thinks the sight, and especially the sound, of the old man "pinioned" and "howling" would drive him insane. However, surely that's better than the alternative, i.e. death for everyone.
In an extremely realistic story, this rather absurd explanation would be a problem. But MD is not pure realism. The white whale itself is a mythical creature that exceeds the boundaries of the animal form entirely. It's the natural world multiplied exponentially, but also something else that can never be defined. Same with Ahab. He's life itself, but he, too, is "extraordinary." No matter how tightly bound he is, Starbuck thinks, that "extra" in Ahab will never be contained. In fact, through containment, it grows even scarier. Starbuck's sanity--and his fear of that thing in Ahab--means more to him than his life, and others'.
Now, is that satisfying? Are we willing to sail on with Starbuck and Ahab and face the white whale? Well, sure. In the first place, it was never up to Starbuck to stop the story's trajectory; it has always been too relentless. It also appears that Starbuck was lost even before this section began--what he's already seen of Ahab, and the universe, has made him willing to trade life for a few more days of not looking into the void. Starbuck has seemed the sanest of all the characters, so if he can't help, no one can.