The Westen Schizm was mostly a political/economic thing. The legitimate and pope resided in Avignon for quite some time, but much of the administration remained in Rome (basically because in the early part of the Middle Ages Rome was a shit-hole) but a pope happened to die while visiting Rome. The Romans took the opportunity to restore the papacy to Rome and the cardinals there elected a new pope, but the administration surrounding the pope in Avignon didn't see the election as valid (for a variety of substantial reasons) and a pope was elected for Avignon. Fourty years went by and there was much confusion as to which was the valid election. Eventually the Roman line prevailed and the names of the Avignon popes from the time of the Schiszm have been re-used by Roman popes since (i.e. the pope elected in Avignon was Clement VII, but there was a Roman Clement VII a couple centuries later). The Church's official line now is that when there are two elections the earlier one takes precedence, but I don't know much about the assertation that the election in Rome was invalid. I don't know what the grounds for that was, but they must have been pretty good, considering that it was the cardinals who were is direct, day-to-day contact with the pope that made the assertation.
So, hypothetically, thing about what it could mean if the fallable, human cardinals bickering over which election counted, decided incorrectly? What if the line in Avignon was the correct line of Apostolic Succession? Clement VII of Avignon had a successor, but that was the end of that line. What if the current line of Roman popes is not in the line of Apostolic Succession?
If you grant that Apostolic Succession is questionable on the grounds of human fallibility (i.e. the human cardinals selecting incorrectly) then can you see how Protestantism and all the branches thereof become equally valid "branches" off the same trunk? Each division forks from the same trunk, each claiming (with the same human fallibility) to have a better grip on the truth than the next branch over.