Skeptics have proposed this question, and it is a legitimate one. If Jesus fulfilled the Old Testament prophecies so well, it would seem that the Jewish people would have followed Him. There are several reasonable answers to this question.
First, the Bible tells us that in the history of Israel, the most common situation was that there was a small subset of the nation, a remnant, who truly followed God. A large part of Jewish history has a small remnant that believed and followed God. Romans 9:27; 11:1-6 teaches this, as does the reading of the Old Testament historical books.
Second, some Jews did follow Jesus, as evidenced by the fact that the entire early church was made up of Jews. The book of Acts (chapters 2 ff.) tells us that thousands of Jews were brought to faith in Jesus as messiah, and gentiles did not enter the church until a good while later (chapters 10 ff.).
Therefore the question proposed to us is a logical fallacy, which has a hidden false assumption, namely that all Jews rejected Jesus.
Third, the Jews that did reject Jesus were largely the leaders. One of these men, Nicodemus, came to Jesus and admitted that in reality, they did know that Jesus came from God (John 3:2). Jewish leaders also knew that Jesus fulfilled prophecy, as demonstrated by their knowledge of His birth circumstances in Matthew 2:4-6. Further, nowhere in the New Testament does anyone challenge Jesus’ right to claim the fulfillment of prophesy. So their rejection was not based on disagreement of whether He fulfilled prophecy.
John 11 gives a significant insight into how the Jews reacted to Jesus. In v.43-44, Jesus raises Lazarus from the dead in front of a group of Jewish people. As a result, the very next verse (v.45) tells us “Therefore many of the Jews . . . believed in Him.” So many Jews did indeed believe, based not only on fulfillment of prophecy but on the actions they witnessed. But v.46-53 tells of the Jewish leaders plot to kill Jesus. Why? They tell us why in v.48-50: They were afraid of losing their positions of power, and afraid of the Romans coming in to attack the nation. Therefore they rejected Jesus not on the grounds of disagreeing with fulfilled prophecy, which they never challenged, but rather on grounds of personal self-interest: they were afraid of losing their positions of power.
Fourth, while this is a valid question if someone were truly curious, the question is usually proposed as a criticism. As a criticism, it suffers from multiple logical fallacies, one of which is what I call the “it seems to me” fallacy. This is basically saying, ‘It seems to me that if Jesus truly fulfilled Jewish prophecy, every Jew would have accepted Him. Since every Jew did not, Jesus should be ignored.’ This does not prove anything, but is merely an opinion or speculation; as we’ve seen, it is a false assumption. It also suffers from the logical fallacy of being a non-sequitur (it does not follow). Just because it seems to you that Jews should have followed Jesus does not prove anything about whether Jesus truly did fulfill prophecy.
In summary, as an argument, this question is logically invalid, since it has false assumptions, does not prove anything, and is a non-sequitur. As a question, it has reasonable answers, namely that Jews did follow Jesus, and the ones that did not follow Him did so due to sinful reasons. Just as Jews did not all follow Moses or any of the Old Testament prophets, some did.