Read these four tutorials, which introduce four major classifications of fallacies. Although there are many possible ways of categorizing fallacies, the four major groups discussed in these tutorials are fairly standard.
Fallacies of relevance are of two kinds:
This includes defending a conclusion by appealing to irrelevant reasons, such as inappropriate appeal to pity, popular opinion, tradition, authority, etc. An example would be when a student failed a course and asked the teacher to give him a pass instead, because "his parents will be upset." Since grades should be given on the basis of performance, the reason being given is quite irrelevant.
Similarly, suppose somone criticizes the Democratic Party's call for direct elections in Hong Kong as follows: "These arguments supporting direct elections have no merit because they are advanced by Democrats who naturally stand to gain from it." This is again fallacious because whether the person advancing the argument has something to gain from direct elections is a completely different issue from whether there ought to be direct elections.
For example, it is not unusual for us to ignore or downplay criticisms because we do not like them, even when those criticisms are justified. Or sometimes we might be tempted into making snappy decisions thinking that our decisions are the best when in fact we should be investigating the situation more carefully and doing more research.
Of course, if we fail to consider a relevant fact simply because we are ignorant of it, then this lack of knowledge does not constitute a fallacy.