In De Cive (The Citizen), Hobbes makes the Argument from Disagreement (AofD) to dismiss traditional moral philosophy (this is from the introductory letter):
"If the moral philosophers had as happily discharged their duty, I know not what could have been added by human industry to the completion of that happiness, which is consistent with human life. For were the nature of human actions as distinctly known as the nature of quantity in geometrical figures, the strength of avarice and ambition, which is sustained by the erroneous opinions of the vulgar as touching the nature of right and wrong, would presently faint and languish; and mankind should enjoy such an immortal peace..."
Hobbes, in typical modern fashion, thinks that the failure of traditional moral philosophy is due to its unscientific character, or its inability to think precisely in the model of the modern natural sciences. The unscientific character of traditional moral argument leads to a diversity of opinion and lack of progress:
"But now on the contrary, that neither the sword nor the pen should be allowed any cessation; that the knowledge of the law of nature should lose its growth, not advancing a whit beyond its ancient stature; that there should still be such siding with the several factions of philosophers, that the very same action should be decried by some, and as much elevated by others; that the very same man should at several times embrace his several opinions, and esteem his own actions far otherwise in himself than he does in others: these, I say, are so many signs, so many manifest arguments, that what hath hitherto been written by moral philosophers, hath not made any progress in the knowledge of the truth; but yet hath took with the world, not so much by giving any light to the understanding as entertainment to the affections, whilst by the successful rhetorications of their speech they have confirmed them in their rashly received opinions."
What indicates the failure of moral philosophy? It's failure to make progress or produce results. Results are the intellectual coin of the realm in the modern world. Knowledge of the law of nature has not grown "a whit" since ancient times. Hobbes adds a new wrinkle to the Argument from Disagreement by citing not only the disagreements among philosophers, but the disagreements of philosophers with themselves.
Hobbes's point reveals a basic misunderstanding of traditional moral philosophy. His point is not new and was addressed by Aristotle long, long ago in the Nichomachean Ethics, Book I, Ch. 3:
"In studying this subject we must be content if we attain as high a degree of certainty as the matter of it admits. The same accuracy or finish is not to be looked for in all discussions any more than in all the productions of the studio and the workshop. The question of the morally fine and the just - for this is what political science attempts to answer - admits of so much divergence and variation of opinion that it is widely believed that morality is a convention and not part of the nature of things. We find a similar fluctuation of opinion about the character of the good. The reason for this is that quite often good things have hurtful consequences. There are instances of men who have been ruined by their money or killed by their courage. Such being the nature of our subject and such our way of arguing in our discussions of it, we must be satisfied with a rough outline of the truth, and for the same reason we must be content with broad conclusions. Indeed we must preserve this attitude when it comes to a more detailed statement of the views that are held. It is a mark of the educated man and a proof of his culture that in every subject he looks for only so much precision as its nature permits..."
Aristotle later in the Ethics elaborates on why moral philosophy will not produce "results" or make "progress" as math or the natural sciences do. Moral philosophy addresses ends, that is what is good and evil. But who has knowledge of the good? Does the wicked or dissolute man have a true knowledge of the good? No, it is the wise and virtuous man who has a true understanding of the good. Unlike math, which can be understood equally well by the evil man as well as the good man, only the good man can truly understand moral philosophy. The education of character, then, is a prerequisite to a true understanding of moral philosophy. The best things in life like love, friendship, justice, honor and magnanimity, are only truly known through experience, and therefore only the man who has lived well for some time can truly know them. The Nichomachean Ethics is not a work addressed to evil or skeptical men, as though they can be forced to acknowledge what is good and just. It is a book addressed to men of good character as a way for them to understand themselves in their virtue, and to point the direction to others who already have some education in virtue. It is natural that there should have been and always will be disagreement about good and evil, for to the bad man evil appears good and is experienced as pleasant. Aristotle even shows why moral philosophers disagree with their own philosophy from time to time. As they mature in virtue and wisdom, they come to a greater knowledge of the good, and from that deeper knowledge they have a foundation from which to criticize their own prior philosophy. But, as with the Argument from Disagreement in general, the fact of disagreement over moral philosophy proves very little.
Interestingly, Hobbes himself argues against the AofD shortly after the passage I quoted above. In his Preface, he lays the groundwork for his famous doctrine of the "state of nature", and that in the state of nature all men distrust and dread each other. He anticipates objections:
"You will object, perhaps, that there are some who deny this. Truly so it happens, that very many do deny it. But shall I therefore seem to fight against myself, because I affirm that the same men confess and deny the same thing? In truth I do not; but they do, whose actions disavow what their discourses approve of. We see all countries, though they are at peace with their neighbors, yet guarding their frontiers with armed men, their towns with walls and forts, and keeping constant watches. To what purpose is all this, if there be no fear of the neighboring power?...Can men give a clearer testimony of the distrust they have each of other, and all of all? How, since they do thus, and even in countries as well as men, they publicly profess their mutual fear and diffidence. But in disputing they deny it; that is as much as to say, that out of a desire they have to contradict others, they gainsay themselves."
Hobbes invokes the principle that disagreement is meaningful only if there is good reason for it. And he cites the prudential defensive measures that individual men as well as cities take as evidence that the objectors themselves don't really believe in their objection (bringing into play the distinction between the public and private books of philosophy.)
And, of course, a similar principle holds with respect to Hobbes's use of the AofD to undermine traditional moral philosophy. That disagreement is meaningful to the extent that there are good reasons for it. But, as we see from Aristotle, disagreement is to be expected as a matter of course in moral philosophy.