It's not like Time's arrow.
Infallibility is a dogma that nobody should need. If the arguments are good enough, they stand on their own. If they aren't then infalliblity won't help. Well, maybe it helps claims that are insufficiently justified (e.g., the Assumption of the Blessed Virgin Mary). For claims that have counterarguments, infallibility is useless; the counterargument itself serves as proof that infallibility is falsely claimed.
Which leads to a further conclusion. It is necessary to consider the bad theology (a.k.a. heresy) as well as the good; otherwise, you can't understand the good properly, because it forms in relationship to the bad. Nicene orthodoxy makes much less sense if you don't understand Arianism and the other errors to which it is the answer. Hence, theology consists in large part of seeing the pathway through all these arguments. And it seems to me that the orthodox tradition-- not necessarily the Eastern version thereof-- demonstrates itself to be essentially correct. Most ancient heresies, when espoused by moderns, are invented anew, particularly Arianism, which the Jehovah's Witnesses reinvented.
When you look at the details, however, the picture of inevitable progress gets severely muddled. At this late hour I see a lot of "doctrine" that has severe problems when held up against the words of Jesus. It is not too much to ask that the two be consistent. To get back to the dog: Jesus never says that dogs are unclean. But he does lift up the first great commandment. Now Nick; if you used a guide dog, would you want someone to take it from you on such a pretext?