The Hypocrisy Fallacy
The Hypocrite Has a Point trope can refer to a Logical Fallacy whereby an argument is dismissed on the grounds of hypocrisy regardless of its own merits, or where the importance of hypocrisy is otherwise exaggerated. In other words, just because someone is a hypocrite does not mean they are wrong, and in many cases, the "hypocrisy" in question is either irrelevant or even only presumed. There are several reasons why this line of reasoning constitutes a logical fallacy, or otherwise as an unfair line of reasoning.
Ad Hominem
Calling someone a hypocrite can be a form of ad hominem attack — that is, you are attacking the character of the debater rather than addressing their points.
Association Fallacy
The Hypocrisy fallacy can take the form of guilt by association — the person making this argument is a hypocrite, thereby anyone who makes this sort of argument is also a hypocrite, or the argument itself is somehow "tainted" by the hypocrisy of the debater. This sort of fallacy usually applies when a member or members of a group are shown to be hypocrites and this portrayed as undermining the entire group or their cause, rather than at best simply questioning the motivations or honesty of the specific individuals.
Black-And-White Fallacy / Speciest argument
The person is a hypocrite and therefore they are utterly in the wrong with no excuses accepted. This is the fallacy of the Principles Zealot (or of one pretending to be) and results in either the argument or the debater being dismissed out of hand; it is when the supposed hypocrite is being held to unrealistic standards so that even if they were forced to commit hypocrisy even just once by unusual or extreme circumstances, they or their arguments are seen as forever tarnished. Often a sign or either dishonesty or madness on the part of the accuser, especially if they are hypocrites in their own right.
Double-Standard
The person accusing the debater of hypocrisy is themselves guilt of hypocritical behaviour, sometimes even the exact same behaviour as the supposed hypocrite; the "it's okay when I do it" defence. Sometimes justification is offered for this, usually in the form of appealing to moral standards of power relations, but often this does not apply- this fallacy can take different forms:
X= Hypocrite Y= Accuser
a) The person in a position of power / moral authority is the hypocrite X, so the accuser Y is either not in power or in a weaker position somehow. Y argues that their own hypocrisy does not matter because they are not the authority, while X should be held to account because of their responsibilities. This can be fallacious if Y is not considering (or simply dismissing) external pressures or stresses that actually come with the position of authority that either compel or perhaps even require them to act in a (real or imagined) hypocritical manner, and it especially applies if Y is mistaken and Y's own hypocrisy is just as significant or moreso.
b) The reverse- accuser Y is in the position of authority or power and X is the hypocrite. Y makes the case that The Chains of Commanding, the burden of power or changing circumstances permit or force them to act in a hypocritical manner, while Xs lack of power not only fails to permit them to be hypocrites but actually robs them of any excuse to be so. This is the opposite extreme of argument a) but it applies when Y is simply using this as an excuse to absolve their own hypocrisy and / or condemn X for their own, especially if it has no real bearing on the matter at hand.
False Equivalence
This is the fallacy of one side being clearly in the wrong rationally or morally, but the other having their argument or character dismissed solely on the grounds of hypocrisy. The classic example in fiction is one side being Always Chaotic Evil against an enemy who is Always Lawful Good, except that due to the stresses of the conflict the latter compromises their ideals in some way and is seen as almost exactly as wicked as the former for it, even if the compromise was relatively minor by comparison- this is the common fallacy of the Stupid Neutral and the excuse of the Card-Carrying Villain (i.e. when they say At Least I Admit It ), who either sees themselves or is seen as somehow more "honest" or "consistent" in their behaviour, forgetting that this hardly matters.
In practice this particular variation of the fallacy tends to depend upon the personal biases or prejudices of the accuser — in other words, the accuser is often a hypocrite themselves for making it, as it often requires Insane Troll Logic, Jerk Justifications or Moral Myopia to work, or it may depend less on the actual hypocrisy itself but rather how or when the hypocrite is discovered or what reasoning they offer.
This mostly applies to clearly defined black-and-white cases; more morally gray circumstances are harder to quantify. It is not a fallacy if the hypocrite is simply held to account or asked to consider their actions, but rather when the hypocrite is portrayed as equal to or worse than their counterpart, especially if the counterpart is somehow seen to have the moral high ground over this.
No Changes Accepted
A person has been guilty of something in the past but decides to change their ways or at least protest against behaviour they themselves are guilty of and sincerely regret, yet they are accused of hypocrisy and they or their arguments dismissed even when they themselves admit that they were in the wrong before, making it debatable if they are truly hypocrites and either way being irrelevant to their argument. Or, essentially, anytime somebody changes their mind they are seen as being a hypocrite even if they aren't or if it doesn't matter to their argument (note: this can be justified if the hypocrite in question is using "I changed my mind" or "I'm making an exception" merely as an excuse rather than being sincere, as long as this has some kind bearing on the merits of their argument).
Straw Hypocrite
The one and only reason the person is a "hypocrite" is that the accuser insists on using particular definitions or strict interpretations of their motives or behaviour. The accuser may have honestly misunderstood what the other person meant or the accuser may be manipulative and disingenuous; regardless, the hypocrite is not truly a hypocrite at all and their position or viewpoint is being misrepresented to paint them as such.
