I know almost no philosophy so please simplify all feedback. While I understand this Analysis for the example, I still don't understand the general, but deeper reasons for the possible failure of transitivity for material conditionals? I rewrite the Analysis here just with the letters:
For brevity, define 'gone' = 'gone to the party'.
Analysis: In this scenario, while it is true that had P gone, then A would have gone,
and it is true that if A would have gone, then M would have gone,
it is NOT true that had P gone, then M would have gone.
If A had gone to the party, P still would not have gone, but M would have gone (because he heard about P's arrest). The first ... and ... second premise[s are] true. This exceptional case proves that this form of argument is invalid, because it overlooks the possibility that
even if P had gone, M would still not have gone...