If one and only one of the Roman Catholic Church's dogmas are refuted by Scripture or logic, then it follows that the entire system falls apart. If the Catholic Church can be shown to not be infallible in teaching, then its claims to authority are not binding on us at all. In that scenario, faithful Catholics would have no choice but to give up Christianity altogether.
In Protestantism, one has to use Scripture and reason to discern truth from error. The ability to make independent decisions exists, with there being options to choose from. That comes with the advantage of a person being able to change his viewpoints in accordance with available evidence.
If, however, one wishes to defend the Roman Catholic Church's claim to infallibility, then he must be entirely consistent. The idea must be defended at all costs. That would place an excessive burden on one to believe ideas that are potentially absurd beyond all measure. This framework would make any thinking person susceptible to apostasy from the faith.