Are Fallacies Subjective?

Hi guys,

So I was explaining various fallacies to a friend and she made this statement: "Doesn't a fallacy depend on what you believe? The detention of a fallacy is flawed." She isn't a philosophy student and this was her first time learning about fallacies, so this question impressed me as, whether she knows it or not, it is hinting at deep epistemic critique. But the philosophy I studied at undergrad and post-grad didn't contain lessons in logic or epistemology (due to what I chose) so I'm not that well-equipped to answer why fallacies aren't dependent on what we believe (or are dependent)... and after this I'm off to research why (or why not).
I'm assuming she's not referring to personal opinions, where an argument is employed to advocate opinion X, rather she's questioning that what we take as 'logical', 'rational', 'fallacious' etc. isn't objectively the case (perhaps isn't a mind-independent truth).
Could anyone help me in understanding and explaining why what's classed as a fallacy isn't subjective or if it is?

Fallacies can be divided into two categories: formal (deductive) fallacies or informal (inductive) fallacies. In the case of formal fallacies, they contain an clear error in form that makes the fallacy objectively a fallacy—or problematic for everyone no matter what they believe. Take the classic:

All men are mortal.
Socrates is a man.
Therefore, Socrates is not mortal.

This is clearly fallacious and objectively, logically incorrect.

But when we get into information fallacies, there is much more leeway for arguing if it is a fallacy or not. This may depend on many factors including intent and context. For example:

Person 1: Why don't you think Superman exists in real life?
Person 2: If you think Superman exists in real life, you are a moron.

Did person 2 commit the ad hominem fallacy? Maybe. She avoided the question and insulted the person making the argument, however, there is a clearly implied "no, I don't think Superman exists in real life" here, so person #2 did not display a error in reasoning.

Informal fallacies are arguments in themselves.

I think she's confusing premises with conclusions.

A logical fallacy occurs when the premises, if true, lead to an incorrect conclusion. The example given by Dr. Bennett above applies.

However, a conclusion based on false premises can lead to an incorrect conclusion, even if the logic structure is not a fallacy:

Socrates is a man.
All men live forever.
Therefore Socrates will live forever.

If the second premise was true, then the conclusion would be correct, thus there is no fallacy in the reasoning. And even if you believe the second statement is true, then logically you must agree with the conclusion. This is why it is important to recognize that the best logic in the world cannot overcome a person who believes in false premises, and why evidence supporting those premises is equally important.