Ignoratio elenchi

Ignoratio elenchi (also known as irrelevant conclusion or irrelevant thesis) is the informal fallacy of presenting an argument that may in itself be valid, but does not address the issue in question. "Ignoratio elenchi" can be roughly translated by ignorance of refutation, that is, ignorance of what a refutation could logically be; "elenchi" (genitive singular of the Latin elenchus) is from the Greek ἔλεγχος, meaning an argument of disproof or refutation. This is one of the fallacies identified by Aristotle in his Organon, and in a broader sense he asserted that all fallacies are a form of ignoratio elenchi.

Example
A typical example of ignoratio elenchi is the argumentum ad hominem, that is the attempt to link the validity of an argument to the reputation (broadly speaking) of the person or the people who support it. However, there exist many other forms of ignoratio; an excellent example is provided by the film Thank You for Smoking:

"Nick Naylor: OK, let's say that you're defending chocolate, and I'm defending vanilla. Now if I were to say to you: 'Vanilla is the best flavour ice-cream', you'd say...

Joey Naylor: No, chocolate is.

Nick Naylor: Exactly, but you can't win that argument... so, I'll ask you: so you think chocolate is the end all and be all of ice-cream, do you?

Joey Naylor: It's the best ice-cream, I wouldn't order any other.

Nick Naylor: Oh! So it's all chocolate for you is it?

Joey Naylor: Yes, chocolate is all I need.

Nick Naylor: Well, I need more than chocolate, and for that matter I need more than vanilla. I believe that we need freedom. And choice when it comes to our ice-cream, and that Joey Naylor, that is the defintion of liberty.

Joey Naylor: But that's not what we're talking about

Nick Naylor: Ah! But that's what I'm talking about.

Joey Naylor: ...but you didn't prove that vanilla was the best...

Nick Naylor: I didn't have to. I proved that you're wrong, and if you're wrong I'm right.

Joey Naylor: But you still didn't convince me

Nick Naylor: It's that I'm not after you. I'm after them."

Red herring
Similar in category, but with darker implications than ignoratio elenchi, a "red herring" is an answer, given in reply to a questioner, that goes beyond an innocent logical irrelevance. A red herring is a deliberate attempt to divert a process of enquiry by changing the subject.

For example:

Topic A is the proposal that academic requirements be raised. Topic B is the possible effects of a budget crisis on teacher salaries. Topic A is abandoned and the unrelated topic B is introduced.

A "red herring" is a debating tactic that seeks to divert an opponent. A digression can, similarly, be a verbal tactic of diversion, but has no place in a serious debate; and the diversion of digression may also be in play.

During a political campaign effort, U.S. President Harry Truman referred to accusations that his administrative policies leaked information to Communist Russia as a political red herring.