What is God's purpose in preventing the believer from understanding certain truths in his word, like when the disciples were prevented from understanding that Jesus would die and rise again?
First let me say that I do agree with that. Probably some are listening who would say, "Whoa. I don't think that was God's problem. I think that was their problem!" This question assumes that God did some preventing. But that's true. It says their minds were blinded. They were kept from seeing for a season (Luke 18:33-34; 24:16).
Answering the question why they were and why we are may not be the same. Let me see if I can answer both quickly.
1) The timing of Jesus' death in a three-year ministry was a delicate matter. He would have been swept away much earlier—either into kingship on the earth, which he did not want, or into crucifixion, which needed to come after three years of teaching—if he had been recognized more openly.
So you have this thing called "the Messianic secret": Jesus was saying, "Don't tell anybody who I am!" They recognize him as the Christ and he says, "And keep quiet," because if the word spreads too quickly there will be this uprising and he'll be swept. And of course to stop that the Romans would come and they'd clamp down on him immediately. And then his ministry would've been cut short.
So he is navigating his way through how much can they know, and how much can they not know. How much information can be released to them and how much not.
And they just need to learn, too, their own sinfulness and how slow, if left to themselves, they would be. Which is, I think, what "preventing" meant: God just didn't give them the illumining power.
2) Now, why would our own insight be slow? Why would my sanctification be slow?
And I'm not sure I know the answer to that, except that God must have his saving, sanctifying purposes in why I'm slow to be sanctified and slow to understand so many things in the Bible.
For me, the way it works is to make me realize how much help I need.
If I were granted in an instant all the insight that I needed to understand every verse in the Bible, then it may well be that I would not have the capacity to understand my own sinfulness, fallenness and finiteness, as I do having to struggle along like a little child learning his ABCs on the way to glory.
So I'm not sure I know why God would hold his insights, and give them at certain points, and then crash us with wonderful insights for a season and then withhold them for others.
God knows what he is doing, and we need to profit from it by acknowledging that we are finite and fallible and sinful.