Definition
The relativist fallacy arises when we illegitimately argue that nobody is incorrect because what is true for you is false for me, and we are both correct.

Examples
1) “2+2=5” is true for me and false for you.
2) “Arsenic is healthy” is true for me, but false for you.
3) “The earth is flat” is true for me and false for you. So, respect my opinion.
4) “Water is composed of nitrogen and corn” is true for me and false for you.

5) "God exists" is true for me and false for you.

6) I know my position is contradictory, but contradictions are true in my way of thinking.

Discussion
Relativism is based on the idea that each culture or person creates their own truth, so nobody is objectively incorrect.

Many people new to philosophy are drawn to relativism because they think all answers are equally good since so many philosophical questions have no final answer. Well, this is false. Imagine arguing the universe was created by a rabbit because we are not really sure how the universe began. The fact that we do not know (i.e. skepticism) does not mean every opinion is true or strong (i.e. relativism).
Now, some ideas are relative. For example, "Green is my favorite color" may be true for me and false for you, and we are both correct. Many intelligent people believe “Kilts are beautiful” is another relative statement since “beauty is in the eye of the beholder.” Einstein proved time is relative, and philosophers debate whether morality is wholly or partly relative.

However, not all ideas are relative. The relativist fallacy arises when we apply relativism to objective areas. The examples in the preceding section illegitimately apply a relativistic approach to nonrelativistic (i.e. objective) fields like math, science, and logic.
So, the fundamental problem with relativism is that truth is not determined by what people believe; “Truth is what is the case” (Ruggiero, 2011).

Relativism is a deep philosophical issue that I cannot fully explore in this work, but I hope it is clear that not all opinions are equal. Again, it is fallacious to argue “my opinion is just as good as your opinion because they are simply opinions” or “2+2=4” is true for you, but false for me. Such statements commit the relativistic fallacy because they confuse opinions with reasoned opinions, skepticism with relativism, and well supported claims with arbitrary claims.

How to Avoid
Remember that believing a claim does not usually make it true or good. Even if everyone believed it, that would not make it true or good.

Remember too that we study logic, science, math, ethics, and many other fields because we believe there are better and worse solutions, true and false beliefs, valid and invalid arguments. If crude relativism were true, there would be no point studying these fields because every opinion would be equally true and good.

Not even the relativistic philosophers adopt this crude form of relativism.

Exercise
1. What is wrong with arguing logic does not apply to me?
2. Explain why the following claim is objective (i.e. not relative): "God either exists or does not exist."
3. Does having an open mind mean "considering all ideas" or "accepting all ideas?"

Answers
1. It seems contradictory to use logic to argue logic does not apply to me.
How can I argue for a position without arguing for it? Am I cutting off the branch I am sitting on?

2. “God either exists or does not exist.” I may not know if God exists, but I know there are only two options: existence or nonexistence.

It is similar to saying “The table in that room either exists or does not exist.” This is objectively true. Even if we cannot open the door or see through a window to verify the table is there, it is objectively true that the table “either is or is not there.”
The statement “God exists” is not made true because someone believes it is true, and the statement “the table in the room exists” is not made true simply because someone believes the table exists. These statements are objectively true or false, even if we cannot determine their truth value.

Many people miss this point at first because they think everyone is right in matters of religion. But this is false. A person’s belief can be incorrect even if nobody knows it to be incorrect. I do not know if the religious or nonreligious folk are incorrect about God’s existence, but I know someone is incorrect since God cannot both exist and not exist.

Finally, do not confuse ambiguity with relativism. The fact that there are different conceptions of God (i.e. ambiguity) does not mean all conceptions are relative. Once two people agree on a certain conception of God, they can then examine the arguments for and against this God’s existence.

3. I think it is best understood as “considering all ideas.” If you accept all ideas, you believe the earth is both flat and round. You believe “It is best to invade Iran” and “It is not best to invade Iran.” Surely, you do not accept all ideas. If you disagree, then you reject my idea that you don’t accept all ideas…. and therefore you do not accept all ideas.