Why did Mr. Starbuck order the men to go after Moby Dick after Captain Ahab died?

Based on the stated premise of this question, perhaps a more careful reading of Moby Dick might be advisable. There is no evidence that Starbuck, the stalwart first mate of the Pequod—the vessel in pursuit of the eponymous white whale—gives instruction of any kind to the ill-fated members of the crew at all, following the death of Captain Ahab.
Toward the beginning of chapter 135, the final chapter of the classic novel, a teary Starbuck begs the obsessed Ahab not to lower the boats once again, to continue a failing battle with the great whale. After a hellish chase, Ahab become tangled in the line of a harpoon he's just sunk in Moby Dick, and is dragged to a watery death. This incident occurs at the very end of this chapter, and neither Starbuck nor any crew member makes an appearance in the book thereafter.
So, again, it might be best to re-read this part of the book, and then rephrase any questions that might remain.