Perhaps it's just me and my zero study of philosophy, but the sentences at Counterfactual Fallacies look too long and incomprehensible! E.g.
what's the "first premise" that I bolded?
what's the "second premise" that I bolded?
I abbreviated the names and shortened some of the words like changing "go to the party" to just "party".
The Problem: An argument is invalid if and only if all of the premises of the argument can be true and the conclusion false at the same time. The pattern of reasoning above does not guarantee a true conclusion when the premises are true. We can imagine an exception to the pattern, which would illustrate that it does not guarantee a true conclusion given true premises. If we can produce such an example, we can never trust this pattern of reasoning as a guarantor of truth.
Scenario: A loves P and P loves A, they do most things together, but their love is so secure that they don't do everything together. Sometimes A parties without P. M loves Anna too and he chases after her whenever P is not around. P despises M and threatens to hurt him because M follows A around. M fears P, so M never risks meeting P. On the evening of the party Pablo was in jail, so he isn't able to party with A as they had planned. A decided to party anyway but did not (because her bicycle had a flat tire and it was too far to walk). Had A partied, M would have gone since he knew P was in jail.
Analysis: In this scenario, while it is true that had P partied, then A would have parties, and it is true that if A would have partied, then M would have partied, it is not true that had P partied, then M would have partied. If A had partied, Pablo still wouldn't have partied, but M would've partied (because he heard about P's arrest). The first premise is true and the second premise is true. This exceptional case proves that this form of argument is invalid because it overlooks the possibility that even if P had gone, Miguel would still not have gone. Notice, however, we may avoid the fallacy if we could assume that if A would have gone, then P would have gone. Sometimes by adding another premise we can rule out all cases where transitivity fails. But in this scenario, we need not make that assumption.
Conclusion: Transitivity does not always fail for counterfactual arguments, but since it does sometimes, hypothetical syllogisms are unreliable and thus invalid.