I think it was Robert Benchley who once said that there were two kinds of people in the world: those who divide the world into two kinds of people and those who don't. Regardless of whether he was right, one thing is certain: there are two sorts of questioners in the world.
The first sort are those people who ask questions to keep from finding things out. These are seen, for instance, in the children who ask "just one more question" in order to keep from finding out it's bedtime or bathtime. Stories with which children couldn't be bothered earlier in the day suddenly acquire a dazzling fascination at ("Just one more time!"). Questions of philosophy ("Why do I have to go to sleep?"), theology ("Who made God, Daddy?"), meteorology ("Why is the sky blue?") and many other fields of human inquiry suddenly become intensely fascinating. And what caring parent wouldn't take time to answer them all one by one-till the danger of a bath or bedtime is past? (Sadly, I number among these cold and callous parents, but no doubt I am in the minority.)
Asking questions in order to keep from finding things out is, alas, not simply the province of children. Such questions are also, more terribly, seen in the enemies of Jesus who asked incessantly for one more miracle, one more sign, in order to keep from facing the fact that he was the Messiah. John tells us, for instance, that some of Jesus' countrymen came to him, having witnessed miracle after miracle and still they asked, "How long will you keep us in suspense? If you are the Christ, tell us plainly." Jesus answered them, "I told you, and you do not believe. The works that I do in my Father's name, they bear witness to me; but you do not believe" (John 10:24-26). It was not that they couldn't tell, it was that they didn't want to know. Some even perversely went so far as to attribute his healings and power to Satan. For such doubt, Jesus has nothing but the harshest condemnation, for it asks questions, not to find truth, but to avoid it.
However, there is another sort of question which can be asked in cleanness of conscience and in the earnest pursuit of the truth. One example of it is seen in the Blessed Virgin Mary who asked "How can these things be?" because she genuinely wanted to know. To the extent she was able to understand, God was happy to answer her question.
Likewise, St. Thomas the Apostle (and his namesake, St. Thomas Aquinas) embodies this sort of questioning faith that seeks understanding. Both Thomases sought the truth in faith and both were answered by Christ with a resounding, "You asked for truth, you shall have it!"
What is particularly remarkable about the Apostle Thomas is how deeply Catholic he remained, even in his doubt. The modern conception of religious doubt dictates that in order to find truth about God, you have to get as far away from the Church as possible and work it out on your own. "Truth" equals "what's true for me."
But John's gospel (and Thomas) tell a different story. There, we find that Jesus appeared to the disciples (minus Thomas) on Easter and breathed on them in a sort of "little Pentecost", giving them the Holy Spirit. This done, it was no longer a gaggle of disciples, but Holy Church, that told Thomas "We have seen the Lord!" And Thomas, though doubting the Resurrection, did not reject the Church. He stayed with them. In so doing, whether he realized it or not, he did not reject Jesus but stayed with him too, for it was Jesus himself who said to Holy Church "He who listens to you listens to me." Thomas was faithful to Jesus himself in the way that mattered most, which is perhaps why, when Jesus did appear to Thomas (in the midst of Holy Church, of course), it was Thomas, the doubter, who was graced before all the other apostles to see Jesus for who he really is: "My Lord and my God."
The same principle applies today. The Christian who says, "I love the Lord! It's the Church I refuse to listen to" is a Christian who, according to our Lord himself, is refusing to listen to the Lord. Conversely, the questioning Catholic who fears he is faithless to Jesus, yet refuses to depart from the Church and does his best to obey her teaching is, whether he realizes it or not, pleasing to God. It's one of the striking paradoxes that springs from the fact that the Word is still made flesh. We find God, not in some disembodied realm, but where he still reveals himself: through the Body of Christ and its tradition and sacraments.