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Moving the Goalposts
Imagine you’re about to kick a field goal. You line up your kick perfectly, and it’s heading right on target to clear the uprights. Just as the football is about to pass through the goal, someone picks up the goalposts and moves them ten yards to the left. This is the idea behind the ‘Moving the Goalposts’ Fallacy. Here’s an example that a theist might use:

Theist: “Show me an example of a transitional fossil!”
Atheist: “Homo habilis.”
Theist: “That’s not a transitional fossil! Show me a fossil of a fish that turned into a human!”

In this example, the theist has asked for a transitional fossil. Technically, all fossils are transitional fossils, but for the sake of the argument we’ll consider that what the theist is asking for is an example of a fossil that can be clearly demonstrated to be a bridge between one species and another. The atheist in the above example has satisfied the requirements by offering a commonly accepted transitional primate fossil: Homo habilis. The theist then ‘moves the goalposts’ by manufacturing an ad hoc redefinition of ‘transitional fossil.’ There are no transitional fossils demonstrating a fish turning into a human (fake mermaid fossils aside) because there were several million transitional steps between humans and fish. So the theist’s demand is shifting the goalposts from the scientifically accepted definition of ‘transitional fossil’ to a patently absurd definition only used by the scientifically illiterate.
The way to defeat a ‘moving the goalposts’ fallacy is to note what the theist is trying to do by explaining how they’ve shifted the goalposts. The way to do this in the example above would be to simply state that of course there are no transitional fossils between fish and human, since the theory of evolution does not say that fish turned into humans in one step.
Once you’ve done that, you may move the goalposts back to where they should be, and start over. The way to do it in the above example would be to explain exactly what a transitional fossil is, and why it’s transitional.

Genetic Fallacy
This fallacy is an attempt to discredit an idea based on the person or situation that ‘birthed’ the idea in the first place (hence ‘genetic,’ which means ‘birth’). Here are a few examples:

“Adolf Hitler came up with the idea for the Volkswagen. Therefore if you drive a Volkswagen, you’re a Nazi.”

“Evolution led to Social Darwinism, and that led to Hitler! So evolution is to blame for Hitler!”

“You’re an atheist, so anything you have to say about religion is irrelevant!”

“I was brought up to believe in God, and my parents told me God exists, so He must.”

The way to defeat a Genetic Fallacy is to focus on the validity or invalidity of the idea itself, and not on the origins of the idea. The truth is the truth no matter who speaks it. Conversely, a lie is a lie no matter who speaks it.

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False Analogy
In a proper analogy, two things are shown to be similar. Let’s call these things, Thing A and Thing B. In a proper analogy, it is argued that since Thing A has property X, and that Thing A and Thing B are similar, then Thing B must also have property X.
Here’s an example of a proper analogy:
Let’s assume Thing A is a male human. Let’s further assume that Thing B is a female human. The area of similarity here is the quality of being human. We then infer that since Thing A, being a male human, is a bipedal hominid, then Thing B, being a female human, is also a bipedal hominid.
An analogy becomes a false analogy when the two things, A and B, are different in such a way that they do not both share property X. Using the analogy above, Thing A is a male human, and Thing B is a female human. Since Thing A has a penis, can we infer that Thing B also has a penis?
An example of a False Analogy that comes up quite often in theistic debates is as follows:

A religion is a strongly held belief.
Christianity is a strongly held belief, therefore Christianity is a religion.
Atheism is also a strongly held belief, therefore Atheism is also a religion.

Obviously the above is a false analogy because of the definition of the word ‘religion.’ Religion is defined as ‘a belief in and worship of a god or gods.’ The original Latin is ‘religare,’ which means, ‘to bind again.’ In other words, if you have a religion, you are ‘binding yourself to God.’ Atheists have no god to bind themselves to, therefore atheism is not a religion.
The way to defeat a False Analogy is to discover what Property X is, then demonstrate that Thing A and Thing B do not share that property. You may also demonstrate that Thing A and Thing B are different in ways unrelated to the property, and are therefore not analogous.
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