The secret things belong to the LORD our God, but the things revealed belong to us and to our sons forever, that we may observe all the words of this law. - Deuteronomy 29:29 [NASB]
Has this, or anything like it, ever happened to you?
You: So you admit that God chose, from the before foundation of the world, those who would come to faith?
Some guy: That is what the scriptures say, and I have no problem with that.
You: So you believe that God chooses whom He will save?
Some guy: I do.
You: Yet you insist that Jesus actually died for no one in particular?
Some guy: That's right, I believe that God saves a person because that person chooses God.
You: But that is irrational. You cannot say on the one hand that God chooses, then on the other say that man chooses - there can only be one cause, not two.
Some guy: Well, that's just one of those secret things of God - a mystery we will never understand.
You: The secret things of God are things that God has hidden, not things God has shown but you have failed to rationally understand.
Some guy: You're so arrogant! You think you can understand the hidden things??
You: Um, no, I don't think I can understand the hidden things, rather I think you are using the notion of "the secret things of God" to justify covering your ears when your theology is shown to be irrational, and therefore wrong. A thing isn't "secret" just because your theology chokes on it - that's probably an indication that there is something wrong with one of your assumptions.
Some guy: I guess we will have to agree to disagree.
It doesn't really matter what your conversation was about, as long as it got to the place where some brother or sister was shown a gaping hole in their thinking, and they immediately pulled the "it's a secret thing of God" card on you, then considered you filled with pride and arrogance because your theology wasn't quite as "hole-y" as theirs (pun intended), and finally refused to hear any more about it since they had no intention of being taught anything new, having loved the old wine of ignorance.
This post isn't about who is right or wrong however. It is about using the secrets things of God as a theological "catch all" to insulate yourself from instruction that you don't want to hear. Being teachable is a sign of humility, and humility a sign of maturity. It is good to be convinced in what you believed, but it is arrogant to imagine that because you are genuinely sincere, you are therefore right in everything you believe.
If someone points out something irrational in your theology - don't agree to disagree, that is not how iron sharpens iron - rather humble yourself and open your ears - give that person your full and open attention, make sure that you so fully understand what they are saying that you can not only repeat it back to him and be understood without it sounding snide - but that you also understand how this fits into the rest of that person's theology. Ask questions as though you were the one who was wrong, in fact, as much as is in you - have that kind of heart when you receive instruction (that is, a contrite heart). If after fully understanding the other's position you stand convinced of your own, then explain why it is that you remain unconvinced, and ask the other to show you where your reasoning is flawed. What a blessing it will be if he or she can and does show you some flaw in your reasoning.
If you are the one who is on the receiving end of some irrational theology be firm but patient, and especially guard yourself from taking the role of teacher. Come along side, do not stand above. Don't tell yourself that you can argue someone into a better conviction - all you can do is lay the truth as you know it before their eyes, and God does the rest.
It has been my own experience, that this situation happens more often when each person presumes himself to be the other's teacher.