What is the name of this logical fallacy?

Factual Questions
1

When someone tries to prove that an example is stupid by substituting key words so that the new example is absurd.

For example, when the womens rights movement started, Mary Wollstonecraft published a treatise called “Vindication for the Rights of Women”. Someone then published a parody piece called “Vindication of the Rights of Brutes” which tried to show that since giving rights to animals was absurd, it should follow from this that giving rights to women should also be absurd.

What is this fallacy called?

2

That sounds like a special case of False Analogy to me.

3

I think Irrelevant Conclusion also fits.

4

Reductio ad absurdum?

5

I’d also go with false analogy. Reductio ad absurdum is a valid technique to expose weakness in an argument. It’s not a type of logical fallacy.

6

Non Sequitur.

7

The end result is the logical fallacy of false analogy, but the construction itself is a rhetorical vice — catachresis.

8

“Reductio ad absurdum is a valid technique to expose weakness in an argument.”

Reductio ad absurdum is actually a valid method of proving a logical argument

(by proving that the opposite (of that which you wish to prove) is absurd).