I recently had a post criticised for being fallacious. It also may have been downvoted and/or deleted, which sucks especially because I know my conclusion was correct.
What is a fallacy, and why is it such a big deal?
A fallacy is a fundamental weakness in an argument which can easily undermine the strength of the entire post if left uncorrected. In its simplest terms, your post containing a fallacy means that it (probably) does not say what you think it says, or what you intended it to say.
Fallacies are typically split into two categories: Formal (or logical) fallacies, and informal fallacies. Formal fallacies are those in which the error is due to an objective flaw in the logic presented, whereas an informal fallacy is one where the error is in the premises presented. In either case, the fallacy may be a direct result of an express statement, or simply implied by context.
Often such fallacies are simply caused by ignorance on the part of the poster, but in the worst case they are intentionally dishonest to fool a reader into thinking their argument is stronger than it actually is; this is a tactic often used by amateur debaters and is especially prevalent on polemic/apologetic sites.
We as a site are not for debates or apologetics, rather we are about the academic study of the topic of Islam. Whether due to ignorance or dishonesty, a fallacious argument is just not useful to forwarding academic study (see also the relevant meta post at "How do I write a good answer?").
It's important to note that the Stack Exchange model caters to expert communities. There is a strong correlation between actual expertise in a topic, and the ability to critically understand posts written on that topic.
In other words, even if amateurs can't tell that an argument is fallacious, an expert almost certainly can. And if an expert sees that fallacious arguments (whether from ignorance or dishonesty) are encouraged here, he is unlikely to trust this site to answer his own questions honestly and/or knowledgeably, and is especially unlikely to stay in order to provide honest and knowledgeable expert answers for other people.
As such, posts containing fallacies need to be corrected, even when the drawn conclusion is otherwise correct. Otherwise, they need to be downvoted or, in particularly egregious cases, may need to be deleted entirely.
There are countless fallacies to worry about. As a general rule of thumb for the purposes of this site, any point which is brought up that doesn't properly establish how it helps answer the actual question asked should be examined for fallaciousness.
In my own experience on this site, a number of fallacies appear to be particularly common (please note, this list is hardly comprehensive):
Irrelevant Conclusion: Rather than answering the actual question asked, an argument (which may be in itself valid and sound) is presented to answer an entirely different (and often easier to answer) question; this secondary question is often tangentially related to the original so closely that it can be mistaken as relevant.
Cherry Picking: Collecting and presenting individual examples, often without establishing credibility or relevance, while ignoring counter-examples which are at least as strong if not stronger. Taken together, these give the appearance that evidence supporting a position is more plentiful than it actually is, which in turn generates the false illusion that an argument itself is stronger than it actually is.
Appeal to Authority: Presenting the opinion of a third-party who is considered an authority in the topic as if it is unassailable fact, especially in lieu of any actual argument. Related fallacies which are particularly egregious are False Attribution (presenting a source as authoritative when it in fact is not) or Quoting out of Context (misrepresenting a source in a way that undermines the position they actually making).
Burden of Proof: The argument that one does not need to actually prove ones own claim when confronted, rather the onus is on others to disprove it; this is often used in conjunction with the Appeal to Ignorance (the argument must be true since it cannot be disproven). In general, the burden of proof is always on the person who is actually making a claim; in the case of Stack Exchange, that usually translates to any person who posts an answer being responsible for arguing their point clearly in the post itself.
Genetic Fallacy: The idea that just because an argument comes from an unreliable source automatically renders the argument itself invalid; this could also go the other way, assuming that just because an argument comes from a reliable source automatically renders it more valid (see also Appeal to Authority above). This often results in strong arguments being dismissed entirely or weak arguments remaining unrefuted because of who presented them rather than because of any soundness/validity of the argument itself.
Appeal to Popularity: The idea that just because a belief is widely-held automatically means it's more valid than a less popular belief. This is similar to the Genetic Fallacy above in the sense that it often results in arguments being dismissed entirely or remaining unrefuted simply because they're more popular rather than because of the strength of the argument itself. Similar fallacies would include the Appeal to Tradition (which implies that an older argument is inherently more valid than a newer one) or its inverse Appeal to Novelty (which implies that a newer argument is inhernetly more valid than an older one).
This is a difficult question to answer. If the fallacy is simply one of irrelevance, this can often be corrected by explicitly establishing that relevance, or by removing the irrelevant point entirely. Many logical fallacies, on the other hand, are a result of non-sequiturs — going directly from point A to point C without actually explaining how you got there — and can often be corrected simply by showing your work.
However, if the entire post is underpinned by one or more fallacious arguments, such that the conclusion drawn has no actual support in the post itself, deleting the post entirely and rewriting it from scratch may be your only option.
If you are having trouble knowing how to proceed, you can always ask a new question on Meta to garner the community's advice.