Irrelevant Thesis

Also called

Ignoratio Elenchi
Irrelevant Conclusion

The formal name literally means "ignorance of refutation" -- this is not refuting the opposing position at all, but acting as though you did. It's really a superfallacy, in the same way that "Rule of Cool" is a supertrope; there are a number of fallacies which are all types of "Ignoratio Elenchi", among them all Appeals To Consequences, all Appeals To Emotion, all Strawmen and Red Herrings, Ad Baculum, Ad Nauseum, and all Ad Hominems.

This one probably occurs in a supermajority of all arguments on the Internet. Perhaps the most common is to dismiss an opponent's claim with "well, that's just your opinion." This has the unstated assumption that all opinions are precisely equal no matter what their underlying logic, but it's also irrelevant; of course it's your opinion, who else's would it be?

Also the favourite combat strategy of high school wannabe intellectuals, who are prone to crow "That's a generalisation!" at any opposing statement. Here the unstated assumption is that all generalisations are wrong in all contexts. And it too is irrelevant; of course it's a generalisation. What isn't? (Oops. Sorry. I guess that was a generalisation.)

Thank You for Smoking (novel and movie) has a lot of this.

Looks like this fallacy but is not

When the idea isn't that one side is right or wrong, but just that the argument has reached the point where it's no longer possible. "We don't have enough information, can we talk later?" In other words, the person is arguing to 'agree to disagree'.
When the points being brought up are fundamental to the original argument. For example, in discussing whether video games can be art or not, raising the question "What, exactly, makes something "art?" " may seem like Irrelevant Thesis, but both sides need to know how the other side defines "art" to have any hope of making a strong argument.