1. Terms to Know
Argument: A conclusion together with the premises that support it.
Premise: A reason offered as support for another claim.
Conclusion: A claim that is supported by a premise.
Valid: An argument whose premises genuinely support its conclusion.
Unsound: An argument that has at least one false premise.
Fallacy: An argument that relies upon faulty reasoning.
Booby-trap: An argument that, while not a fallacy itself, might lead an inattentive reader to commit a fallacy.

2. Reasons Arguments May Fail – aka Logical Fallacies –
They might fail because one of the premises is false.
All toasters are items made of gold.
All items made of gold are time-travel devices.
Therefore, all toasters are time-travel devices.
A valid argument follows logic (regardless of whether or not the statements are true).
A sound argument is an argument that is both valid and factually correct.
This argument (above) is an example of False or Faulty Logic wherein the argument follows a valid logic, but the premises themselves are false.

3. Arguments also fail when the conclusion does not properly follow from the premises.
People who study generally do well on tests.
I studied for my chemistry exam.
Therefore I deserve an A in chemistry.
This is an example of a “Non Sequitur” fallacy, in that the conclusion does not follow from the premises OR when an action is justified by making a point irrelevant to that action.
The police chief's reasoning was a non sequitur when he defended consulting a psychic "to help investigators crack the case" based on the premise that "we tried everything else and haven't solved the case yet”.

4. Bill: "Jill can give me a good reference."
Interviewer: "Your resume looks impressive but I need another reference."
Bill: "Jill can give me a good reference."
Interviewer: "Good. But how do I know that Jill is trustworthy?"
Bill: “Because I can vouch for her."
If such actions were not illegal, then they would not be prohibited by the law.
Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This is also known “Circular Reasoning”.

5. Adolf Hitler: This is an irresponsible fiscal policy because the budget deficit is too great.
Politician: I won't listen to you! You're Hitler!
Bob: "This bill will be expensive and will not work, therefore you should vote against it."
Alice: "Bob is employed by a company which stands to lose money from this bill, therefore Bob will lose money and perhaps his job if this bill passes. Of course he would oppose it."
Rich people who help poor people can't truly sympathize with whom they're helping, so they must be doing it for some selfish reason.
Bob: "Smoking and alcoholism are well-known as risks for cancer."
Alice: "But you yourself smoke and drink a lot! You're wrong!"
Ad Hominem, which translates to “against the man/person”, is a fallacy in which a claim or argument is rejected on the basis of some irrelevant fact about the person presenting the claim or argument (aka a personal attack on the person, not a discussion of the argument).
Direct: An attack directly on the person making the argument themselves.
Circumstantial: The attack is on the circumstances surrounding the person making the argument.
Poisoning the Well: The attack on the person is intended to call into question everything they say.
Tu Quoque (you too): The attack is that the person making the argument does the same thing they're arguing against themselves, or that they, at some previous time, held a different opinion.

6. Keanu Reaves is in The Matrix Keanu Reaves is in Speed.
You loved The Matrix.
Keanu Reaves is in The Matrix
Keanu Reaves is in Speed.
You must love Speed.
Affirming the Consequent or Confusing Cause and Effect is when it is assumed that one event must cause another based on certain premises.
In the above example, Keanu Reaves may have had nothing to do with why you liked The Matrix. Even if it did, it does not mean you enjoyed Speed. Too many other factors are involved for this to be logical.

7. Bandwagon Fallacy, or Appeal to Popularity is the notion that popular ideas are necessarily right; when a person/etc. changes their opinion in response to peer pressure.

8. John's iPhone broke after two weeks, so there must be something faulty in the general manufacture of iPhones
This is a Hasty Generalization. A general conclusion that a certain condition is always true based on one instance or observation.
If we legalize gay marriage, next we'll legalize marriage between men and their pets.
Faulty Analogy, comparing two unlike items in a way that suggests they are more alike/related than they actually are.

9. There is no proof that ghosts don’t exist. Therefore, ghosts exist.
Appeal to Ignorance: Supporting a claim merely because there is no proof that it is wrong.
I thought you were a good person, but you didn’t volunteer today.
This is a False Dilemma or a case where only two choices are presented when more exist.
Pollution is destroying our rivers.
We can’t worry about the environment, we’re in the middle of a war!
Attempting to redirect the argument to another issue to which the person doing the redirecting can better respond. Also known as a Red Herring.

10. Keeping a dog as a pet is as evil as human slavery.
A Moral Equivalency, which is the implication that two moral issues carry the same weight or are essentially similar. In the above example, the speaker is equating the treatment of animals with the treatment of human beings.
I wore my lucky jersey during the last two games that we won. Therefore, my lucky jersey won the games.
A Post Hoc or Faulty Causality; Correlation vs. Causation. This comes from the translation for the phrase “after this, therefore because of this”. X precedes Y therefore X cause Y.
Parents often claim that lying will lead to becoming a criminal.
This is an example of a Slippery Slope, wherein a relatively insignificant first event is suggested to lead to a more significant event, which in turn leads to a more significant event, and so on, until some ultimate, significant event is reached,

11.
PBS | The Idea Channel