Definition

False Analogy, also called Faulty Analogy, is an informal logical fallacy in inductive reasoning. It’s a part of Generalizations Fallacies group. It usually occurs when someone applies or assumes that if two things or events have similarities in one or more respects, they are similar in other properties too. Still, the things or events are substantially different, and those similarities can not be extrapolated to other properties.

This logical fallacy is widespread, because real-world parallels are always limited; the differences between things can often overpower their similarities. Sometimes person providing such an argument is not aware of such difference, but very frequently, if aware, they ignore it outright.

Examples:

If professionals are allowed to lookup information in books why students are not allowed to do the same during exams?

Drinking coffee in the morning to wake yourself up is like having a glass of wine to treat a hangover.

Using Analogies in arguments

People use analogies and metaphors because they are easy way to explain some things to others. These literature devices are very important, convenient and popular. However, because of the prevalence of false analogies, they’re much less useful in making arguments.

Metaphors

The Banana Analogy

Bananas and telephones are both shaped to fit our hands, so bananas must, like telephones, be designed.

This is fallacious because the similarity in one area doesn’t imply a similarity in another. For example:

Bananas and telephones are both shaped to fit our hands, so telephones must, like bananas, be edible.

The “watchmaker” analogy

The argument from design, or the The watchmaker analogy is an example of a false analogy used by Creationists (believers in Universe creation by God) when analogy is made between the complexity of a watch and the complexity of the Universe. Here it is:

The Universe is like a watch.
A watch must have a watchmaker.
The Universe, being like a watch, must have a maker designer.

The false analogy can be shown by a reduction to the absurd, highlighting the many differences between the Universe and a watch. Similar absurdities can be built from almost every other characteristic of watches:

The Universe is like a watch.
A watch can be used to cover a tattoo on one’s wrist.
The Universe, being like a watch, can be used to cover a tattoo on one’s wrist.

Irreducible complexity

It argues that there are some things that are so complicated that they could not have evolved or randomly occurred, and therefore a creator must exist. No mathematical or scientific definitions of irreducible complexity have yet been offered, and all examples have been found to have entirely natural explanations.

Argument from fine-tuning

The argument from fine-tuning asserts that the possibility of life coming into existence is so incredibly low that an intervening actor must have caused it, ignoring the evolutionary nature of life and the universe’s hostility.

Argument from beauty

It’s too beautiful to occur accidentally.

Information argument

DNA has information encoded in it. Someone very smart must have done this.

In reality, encoded is just an analogy, and the precursor is DNA, not the properties of the result object.

A typical response to False Analogy Fallacy

When someone notices False Analogy, it’s very usual to hear the reply like:

You are comparing apples and oranges.

It’s meaning - they are both fruits but completely different.

Yes, they are like Cheese and Chalk.

These words starts with the same letter combination but have nothing similar.

If bananas and the sun appear yellow, one could not conclude that they are the same size.

Some definitions and examples are from Texas State University, some are from Rational Wiki, more info: