NOTES for Mat 16:20-24
Not only many Pharisees, but even the apostles themselves did not understand their Teacher in everything. This, in fact, evidently explains Peter's reaction to Jesus' words about His coming death and resurrection. As for death and resurrection, the disciples never did understand Jesus, and only after His resurrection did the situation become somewhat clearer for them.
Evidently both Peter and the other apostles still held more or less traditional views of the Messiah and messiahship. And they did not understand at all how the Messiah could die. The issue here was not even that He would then rise from the dead - the apostles, like all their Jewish contemporaries, of course knew about the general resurrection on the day of Judgment. The issue was that the Messiah could not, must not die, because He was supposed to stand at the head of the messianic uprising in order afterward to lead the holy war for establishing the Kingdom of God on earth.
And when Peter says to Jesus, "May this never happen to You!" he is horrified not so much by death itself (after all, during the Last Supper he would speak with complete sincerity about his readiness to die beside the Teacher), as by the thought that Jesus' mission would turn out to have failed, that none of what he and the other apostles were waiting for would come about. Such a thing simply could not happen, because the Messiah is the one who carries out God's plans on earth; there can be no failure here. Failure is possible in only one case: if this Man is not the Messiah. But both Peter and the other apostles were afraid even to think of that.
That is why Jesus' words about His coming death and resurrection throw them into shock. But, as is clear, apart from Peter no one dared voice his fears and bewilderment aloud, perhaps fearing that he would hear the worst. All that remained was to follow the Teacher and see what would happen next.