When an argument is being discussed in a respectful manner, one party generally advocates a particular position and a person who does not hold the same belief offers counter-arguments and reasons why the claim being made is faulty. Consider, for instance, a proposition that an all-powerful, all-loving, and all-knowing god exists. A person may state that this belief is problematic because of [the frequency of] natural disasters in the universe, no good reason such a being would sit by idly and allow gross moral evil to occur, etc [View my problem of evil posts here]. At this point, the discussion can go many ways. In a civil and reasonable discussion, the person who claims that an omni-god exists would answer the counter-arguments, show why the counter-arguments fail, and he/she may raise some new points. The discussion will go back and forth until the parties end the discussion for whatever reason.
The above example was a general sketch of a civil discussion, but instead of this, the original claimant (or really any party) can see disagreement as some sort of attack or might believe that the person who disagrees thinks that the claimant is stupid. There is no good reason to interpret the situation in this manner unless someone is clearly being a jerk or levying personal attacks. Disagreement in a respectful manner should not be construed as a personal attack.
Disagreement should not be thought of as a complete character evaluation of a person. For example, I might posit idea x and you might disagree with idea x. My reasons for believing idea x may be recognized as faulty by you, but this should [generally, but with some reservations] not lead anyone to the conclusion that my stance on one issue shows that I am, 'across the board,' an idiot. It is important to realize that many people hold beliefs for various reasons including rationalization of certain ideas, lack of exposure to counter-arguments, lack of skepticism, and fallaciously applying different standards of skepticism to different ideas (special pleading).
Many intelligent people can hold some unsubstantiated beliefs and the reasons for holding these beliefs can be really bad ones. For example, one of the smartest living scientists, Francis Collins, interpreted a triune waterfall as a sign from God and, seemingly because of seeing this waterfall, he believes that the Christian god exists. I can formulate a list of various reasons why the reasons for this belief are deeply flawed, disagree with Collins, and have a discussion with him. Although we disagree, this does not mean that I think he is a complete idiot and I am not attacking him in any manner.
Some people might hold beliefs simply because they have not simply are not skeptical or do not have 'critical thinking toolkits.' This was the case, I believe, with me in my childhood to my later teen years. I was not a skeptic and held many beliefs because of what I now think to be grave errors in thinking that I was unaware of. I believed in the Christian god, I think, because it was the 'default good,' I was taught to believe that faith was a permissible and worthy quality, and various authority figures held this belief. Because of this belief, I committed various lapses in thinking such as believing that God healed a sunburn I had and diminished the pain after I prayed (post hoc ergo propter hoc/false cause fallacy), a communion wafer tasted really bad because I ate it before I should have eaten it...and the later ones tasted better (placebo effect, false cause), and God sent a sign that my dead friend was in Heaven after I saw someone who spoke with me the next day wearing a shirt with an obscure band on it that I listened to.
I would not call my earlier self stupid or find him blameworthy because he simply did not know better. Now, with an understanding of logical fallacies and critical thinking skills, I recognize these errors. Another problem with my earlier self is that I never heard or considered serious objections to my belief in God until I was about 16. Soon after hearing objections, I determined that holding justified true beliefs was paramount and I embarked my quest to atheism and skepticism. I understand that many people, while they may be old or young, were and are just like I was; they were largely ignorant of contrary ideas to their positions and believed all sorts of fallacious claims. [Read more about my 'backstory' here.] Mainly because of this, and many other factors outlined in this post, I do not think people are stupid because they hold certain ideas that I disagree with.
Some people may compartmentalize belief; they apply rigorous standards/skepticism to almost every area of their lives, but they don't apply rigorous standards/skepticism to some beliefs they hold. For example, a person can understand that homeopathic 'remedies' are merely diluted substances that have no effect whatsoever and psychics have no real abilities to see the future, but they go to a chiropractor who alleges that he realigns spines with God's ultimate intentions and that asthma and long-term medications lead to a sicker body, amongst many other claims. A person like this, instead, should apply skepticism globally, but he/she does not. He/she may rationalize such a belief and utter statements like "My life was horrible until I went to a chiropractor and I was much better after!" (false cause fallacy, possible placebo effect) without realizing the logical fallacies.
Voiced disagreement rebutting the claims of the chiropracty endorser should not be construed as a personal attack, but rather a situation that both parties (and perhaps more in an 'audience' of sorts) can profit from. A good intentioned person who critiques an argument, instead of attacking the person, is actually doing the person a favor by disagreeing and having a discussion because involved parties are able to test their own beliefs by defending them in an open fashion. Justified true beliefs matter. Those who are able to critique their own beliefs and those of others engage in healthy 'cognitive exercise' and can walk away from a civil and productive discussion fulfilled. Instead of disagreement being thought of as disrespect, it should be thought of, if done in a respectful manner, respect. By taking the time to voice disagreement, I am helping others evaluate their ideas and care enough to voice my criticisms. While it is not always the case that discussions are motivated by good discussion, civil discussions can end as productive and fulfilling.
Some people also believe that disagreement without someone is being disrespectful because people are failing to 'respect beliefs.' In my two years of blogging, public discussion, and commenting in various mediums, I have yet to hear one person give a solid definition (despite my constant asking) of what I believe to be an utterly incoherent concept that is fundamentally mistaken. This phrase is further confusing because the motivations for this phrase are hard or impossible to discern. Does the person really think that no beliefs a person holds should ever be criticized? Does the person think that some topics should be utterly left alone while others are 'fair game'?
I usually, after asking what 'respecting beliefs' means, note that beliefs have no cognition and can't possibly be disrespected, so this phrase makes no sense. I also note that disagreement does not entail that a person is being disrespected (as I've done several times in this post). I firmly believe that all topics should be open to be critiqued and that discussion about important and 'personal' matters should especially discussed. As a society, we do ourselves a great disservice when we fail to discuss important topics.
There is a huge difference between 'attacking ideas' (I'm using this very figuratively here) and attacking persons. When I am attacking an idea, I am noting the weaknesses of the idea, pointing out possible logical fallacies, and noting counter-objections. There is, at no time, and disrespect toward a person...and the person really is only involved as the other party presenting arguments because the idea is what is being discussed. If I were to attack a person, I'd hurl insults, possibly physically harm a person, or talk about how stupid the person is being/is.
Perhaps our language needs to be more careful in order to better 'separate beliefs from persons' and not give people the impression that they are being attacked when there is disagreement (and I need to work at this myself). More use of language should address the argument and not the person, perhaps by saying "I disagree with this argument because" instead of "I disagree with you because." Perhaps the phrase "This argument commits the *insert logical fallacy here*" instead of "You commit the *insert logical fallacy here."
This endeavor, though, is a tremendously difficult one for people who don't already understand that disagreement is not disrespect. Since people hold beliefs, people think of their beliefs as being a part of their character, a result of careful thought processes, and generally place them on a high throne. Very important and cherished beliefs, when challenged, can lead a person to utter rage and a vitriolic manner. Instead of thinking of disagreement as criticism of an argument, some people frame disagreement as a character attack by thinking: "Who are you to disagree with me?" , "You are saying that I am wrong?" , and "Since you disagree with me, you must think that I am stupid."
We can, at the end of the day, walk away from critical discussions as friends. We need not all agree about every given matter in order to be friendly and respect other persons. While living together is more important than agreeing, this should not, for one moment, be a reason to never critique a belief. Persons should welcome discussion and see discussion as an opportunity to put their beliefs to the test instead of viewing discussion as 'argument' and an attack on one's character.