Certainly, in two opposite opinions, if one be perfectly reasonable, the other can't be perfectly right.

For there is hardly any question in the sciences about which clever men have not frequently disagreed. But whenever two persons make opposite judgements about the same thing, it is certain that at least one of them is mistaken, and neither, it seems, has knowledge. For if the reasoning of one of them were certain and evident, he would be able to lay it before the other in such a way as eventually to convince his intellect as well.

People should learn to disagree to agree. There is nothing wrong with disagreeing and arguing out things to get the best results.

Because agreement and disagreement have to do with words and concepts and theories. They don’t have anything to do with truth. Truth is never expressed in words. Truth is sighted suddenly, as a result of a certain attitude.

I do not agree or disagree in everything with either one party or the other. Because all seem to me to have some truth and some error, but everyone recognizes the other’s error and nobody discerns his own.

...when two opposite points of view are expressed with equal intensity, the truth does not necessarily lie exactly halfway between them. It is possible for one side to be simply wrong.

Having some disagreement is normal. It is real, it is human. And it's an opportunity for us as mature beings to work through it

A: "Your objection to the self-evident has no validity. There is no such thing as disagreement. People agree about everything." B: "That’s absurd; people disagree constantly, and about all kinds of things." A: "How can they? There’s nothing to disagree about; no subject matter. After all, nothing exists." B: "Nonsense. All kinds of things exist, you know that as well as I do." A: "That’s one. You must accept the existence axiom, even to utter the term “disagreement.” But to continue, I still maintain that disagreement is unreal. How can people disagree when they are unconscious beings who are unable to hold any ideas at all?" B: "Of course people hold ideas. They are conscious beings. You know that." A: "There’s another axiom, but even so, why is disagreement about axioms a problem? Why should it suggest that one or more of the parties is mistaken? Perhaps all of the people who disagree about the very same point are equally, objectively right." B: "That’s impossible. If two ideas contradict each other, they can’t both be right. Contradictions can’t exist in reality. After all, A is A." Existence, consciousness, identity are presupposed by every statement and by every concept, including that of "disagreement." … In the act of voicing his objection, therefore, the objector has conceded the case. In any act of challenging or denying the three axioms, a man reaffirms them, no matter what the particular content of this challenge. The axioms are invulnerable. The opponents of these axioms pose as defenders of truth, but it is only a pose. Their attack on the self-evident amounts to the charge. "Your belief in an idea doesn't necessarily make it true; you must prove it, because facts are what they are independent of your beliefs." Every element of this charge relies on the very axioms that these people are questioning and supposedly setting aside.

Two people feel strongly about an issue, their feelings come first, and their reasons are invented on the fly, to throw at each other. When you refute a person’s argument, does she generally change her mind and agree with you? Of course not, because the argument you defeated was not the cause of her position; it was made up after the judgment was already made.

Logic and truth are two very different things, but they often look the same to the mind that’s performing the logic.

You can either agree with me, or be wrong.

Suppose you and I have had an argument. If you have beaten me instead of my beating you, then
are you necessarily right and am I necessarily wrong? If I have beaten you instead of your beating me, then
am I necessarily right and are you necessarily wrong? Is one of us right and the other wrong? Are both of us
right or are both of us wrong? If you and I don't know the answer, then other people are bound to be even
more in the dark. Whom shall we get to decide what is right? Shall we get someone who agrees with you to
decide? But if he already agrees with you, how can he decide fairly? Shall we get someone who agrees with
me, how can he decide? Shall we get someone who disagrees with both of us? But if he already agrees with
both of us, how can he decide? Shall we get someone who agrees with both of us? But if he already agrees
with both of us, how can he decide? Obviously, then, neither you nor I nor anyone else can know the answer.
Shall we wait for still another person?

All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others.

When men and women agree, it is only in their conclusions; their reasons are always different.