Benignuman,
So I guess that you are infallible, if you think your opinion is more likely to be right than theirs.
If R’ Schach or the Chazon Ish say a pshat which I “disagree” with, I break my head to try to understand it, because I know that they’re much more likely to be correct than I am.
Even more to the point, if my rov gives a psak which I don’t “agree with”, I follow it nonetheless. This is actually a better analogy in one sense; the decision to join the army or not is very much a halachic one.