When making sense makes no sense
Since logical fallacies have been employed so routinely and repeatedly in comments here, the "straw man" being a particular favorite of certain commenters, I found this bit on Daily KOS on "false dichotomies" of interest.
A list of logical fallacies with brief descriptions is found here, while for a more extensive and in-depth exploration, go here.
In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).Look over the list. Which have you seen employed here or elsewhere? I've probably used a few myself.
A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true.