I understand that one must often say (and devoutly hope) that 'God knows better'. And you can strongly discipline yourself to try your hardest to examine your beliefs. But I do not understand how anyone can brainwash themselves into believing something they do not.
There are those things in faith that we accept knowing we cannot understand them, knowing that they simply cannot be completely comprehended by our reason. Then there are those things that are to do with morality, which are not inherently irrational. We are taught that it is wrong to murder; we (I hope!) accept this as something that is not only doctrine, but also something we can rationally and intuitively agree with. We are also taught, when someone we love dies or something terrible happens, that we do not and cannot let our own natural, sorrowful reactions outweigh our faith that God acts for the best.
But here, we are really being asked to accept the limitations of our own knowledge. That's easy. What I do not think is possible, is to truly eradicate a belief in one thing from your mind and replace it with the opposite. You might do it over time, by reason, but you can't just will it to happen.
I think the division you are making is somewhat artificial. Yes, there are things we will never understand (because of our limited, creaturely nature) and things we can, at least in theory, understand and its important to recognize when things fall into the first category. At the same time, it is the teaching of the Church that human nature is fallen and broken. Our will and our desires our corrupt, such that we desire things that are not good for us, and even when we desire to do good, our will is overcome by other desires and we do wrong. But a further consequence of the Fall, which is not as generally recognized, is that our intellect is also fallen and corrupt. We think things are a good idea when they are not. We think things make sense when they do not. There are human societies (fewer now, but their existence is well documented) where cannibalism or human sacrifice were considered completely rational and moral behaviors.
We look at a society like the Aztecs and are appalled. But based on what they knew, and the entire complex of beliefs and presuppositions their society had built up over time, the sacrifice of thousands of people was a perfectly rational behavior. We are not immune to this. If one does not believe the fetus is an actual human being, it makes sense (or is at the least reasonably arguable) to prioritize the rights of the woman over her body over the potential of any particular clot of cells inside her. Our societies come with their own inbuilt assumptions, mistaken perceptions, and biases which make what is 'perfectly obvious and reasonable belief' to you, decidedly questionable to me.
Thus submission to God (through the Church) involves a submission of not only the will but also of the intellect. I don't mean you turn off the intellect. But it does mean you do not presume that your intellect, your logical conclusions, your 'reasonable' beliefs, are superior (or even necessarily equal) to the intellect, logical conclusions and reasonable beliefs that the Holy Fathers and Mothers which preceded us where led into by the Holy Spirit.
I did not, btw, mean to imply that one can simply will the eradication of a belief. However, one can will to work towards that. One can by will, decide that one is simply not going to actively push back against the Church. One can pray for guidance--instead of praying that others see your point or that you are given the words to convince them, pray that you can be led to an understanding. One can repent (I though Thoughtful's priest was very wise).
Or, just to use a completely separate example: We know that you are in a long-term, committed relationship. This may well have already happened. If it hasn't, then I can guarantee you it will. At some point, you are going to have to decide that you believe your significant other, or you don't. That decision may be influenced by what has happened in the past, by the specific circumstances, etc. But in the end, that faith and trust will be a *decision* made by your will in the absence of enough information for it to be made simply by your intellect.