In this post, I will focus on what makes an argument, how to fight it, and what to fight. To start somewhere, I will make an example. You can dislike Obama because he is a lefthander. No matter how wrong this is, you can do it. It is your personal preference. What you cannot do, is dislike Obama's reforms because he is a lefthander. Now, those are two totally different things, that have nothing with one another.
First things first. We shall start with the one that writes the initial argument, as this is where all the discussion will originate from. It is of paramount importance for the writer, to be as concise and as clear as possible. I will admit that at times, the concise part of writing eludes me. It comes down to clarity. If everything is easily understandable, it will be easily remembered. Thus we will all know what we are talking about.
Ones thoughts are his arguments, his opinion on the matter at hand. Opinion as such, cannot be either right or wrong. It is. This is where it ends. No matter how much you agree with it, or disagree with it. Thoughts as such, are. They are, and nothing more, and nothing less. Now, what is most important about argument is the soundness or validity of its claims. This is where things get interesting.
While with argument as a whole you can only agree or disagree, you can tear apart the argument on the basis of its validity. In this validity fall any kind of contradictions, logical fallacies, and other kind of mistakes. The whole basis for this is Informal Logic. Fallacies as such are especially problematic, because they are considered a fruit of poor reasoning.
One particular fallacy I would like to bring your attention to is Ad Hominem. The argument against person. You should always play the argument itself, never the individual behind it. I would also claim this is the one fallcy that plagues the Internet as a whole the most.
Just because someone would say: (and this is example, I am just demonstrating here) "Men are superior to women.", does not mean, that you can retort back with: "You say this because you are privileged man". This only leads to further dilution of the original argument. And because the initiator got you to committing a logical fallacy, you just lost, fell into his trap, even if there is (or might be) one such fallacy even in his own saying.
Now, you might be wondering what would be the right response. For starters, ask him to elaborate. In what sense does he think men are superior to women? As the discussion goes, you might discover that he is either stuck in his ways ( I am trying really hard not to write an idiot here), or that he just did not specify enough in original post. And he meant what he said in some context, such as sports for example. Yes, not being specific enough in first place is his fault as well, but better safe than sorry.
I would argue that trying to persuade others into your own thinking is a fallacy as well, but that is just my opinion, so you are free to ignore it. I see persuasion as means to further your own agenda. As such, it comes very close to personal gain, and politics. A good argument can and will stand on its own. A good argument will attract people on its own. It does not need promotion, pity, or help to achieve what it sets to achieve.
I would recommend reading more on Logical Fallacies here. It is concise and entertaining way of explaining the mistakes in argumentation. Most of these are no-brainers, but they can become quite common once you fall into a deep discussion. It is important to leave feelings out of this. They should never play any role in a proper discussion. People can get pretty riled up when there is a topic they feel very particular about. And this is understandable, we are humans after all. We live, we breathe, we feel. Yet, if any kind of discussion is to be, feelings need to wait outside. They play no role here, and are only in the way.
About arguing itself, I would recommend staying at topic. Do not stray, or try to broaden it, to include more into the original than there is. Do not attempt to focus it down a specific route if this is not where the argument is meant to be. In short, focus on the pure argument as it is. Not on what it might be, or what it could be. This will lead nowhere, and some people might be insulted, or convinced that the one they are having this discussion with is evading the topic.
And while person B might feel ignored, person A is wondering what is this carrot on a stick, and into what trap it might lead. Thus person A will opt to leave it as it is, and focus on what he feel is still relevant in relation to the topic at hand.
I hope this was of help to some, and maybe a moment of introspection for others. In general, I want to see a healthy discussion that focuses on the topic. I believe that if we know how to engage in conversation, and to what we should be paying attention, the discussion can be much better than just plain disagreement or agreement with the writer. Blogging as I see it, is about sharing your opinion with the world. Our duty of sorts, to promote a good discourse through our community.