Trying to figure out the fallacy here, I can't put my thumb on it.

Person A: I believe there are only two genders.

Person B: Why do you say so?

Person A: Because NO ONE'S ever proven that there are more than two

Now, I'm rather sure that there's a fallacy here but I don't know which, somebody help?

Argument from Ignorance . The assumption of a conclusion or fact based primarily on lack of evidence to the contrary.

Scientifically, this is a strange dialog because gender (not biological sex) is a socially constructed concept to which no "proof" can exist outside of wide-scale agreement. A gender is XYZ because we, as a society, has agreed that it is.

It does sound like argument from ignorance (see Kahane, Logic and Contemporary Argument).

But there may also be a false dilemma. The argument assumes that only two choices are possible. (Getting into factual area here, many scientists have researched various intersex sates.) When someone tells you in a loud voice that there are only two choices, caution is advised.

The claimant prefaces his or her statement with "I believe" which neutralizes the claim.
It is simply a statement of belief.

The belief states there are only two genders and thus
through its ambiguous use of the word, gender creates a Fallacy of Amphiboly.

Linguistically, an amphiboly is a type of ambiguity that results from ambiguous grammar, as opposed to one that results from the ambiguity of words or phrases—that is, equivocation. Logically, the fallacy of amphiboly occurs when a bad argument trades upon grammatical ambiguity to create an illusion of cogency.

As Dr. Bo describes:

Ambiguity Fallacy

(also known as: ambiguous assertion, amphiboly, amphibology, semantical ambiguity, vagueness)

Description: When an unclear phrase with multiple definitions is used within the argument; therefore, does not support the conclusion. Some will say single words count for the ambiguity fallacy, which is really a specific form of a fallacy known as equivocation.

Logical Form:

Claim X is made.

Y is concluded based on an ambiguous understanding of X.

My interpretation of the statement:

Assertions without proof are absolutely True.

If I may cheat with an equivalent model:

Person A: I believe that God exists.
Person B: Why do you say so?
Person A: Because no one has ever proven that God does not exist.

I am reading LF for the first time, so I have no idea which one of the 300 violations this fits.