Reform Judaism/Messiah and messianic Jews
Why don't Orthodox Jews believe in Jesus like Messianic Jews do?
Thank you for your kind question. You asked "Why don't Jews believe in Jesus?"
The short answer is that the world has yet to be redeemed. You would have to agree the world is in no better shape (and one might argue worse) than when Jesus was here.
The slightly longer answer is that he (nor anyone) did not fulfill the messianic prophecies. As a Christian you no doubt believe that G-d gave prophecies to the prophets so they would know when messiah had come. Let me use this analogy: If I told you that you would be at my house when you went to the end of road A, turned right and parked in the drive of a yellow house with and American flag outside. Now, if you simply drove to the house next door to yours (blue, not anywhere near road A and an Autumn flag was flying outside) would you say "I'm at Ovadiah's house"? Of course not. You likewise would not say "Well I'm not at his house right now but this will be where he builds his next house". So it is with the specific happenings that will occur during the messianic age. You can look up the specific prophecies using any search engine.
You also asked about messianic Jews. I, personally, do not believe you can mix our two faiths. From our world view to our understanding of G-d and His commandments we're not even in the same neighborhood. For anyone to believe that the Jews of Auschwitz went from the fires of the ovens to the fires of hell (because they did not believe in Jesus) is an anathema. For a so-called Jew to believe such a thing is a disgrace. In most Jew's opinions, there is no such thing as a messianic Jew. While I applaud their embracing the Jewish heritage, I can more more rename myself Vinnie and start eating pepperoni pizza and call myself an Italian.
As a Reconstructionist Jew I believe that we all play the messiah role in bringing about world peace, justice for all, compassion and empathy and the realization that we are all Children of the Most High and created in His image OURSELVES. G-d isn't going to do it, but we will know for absolute certainty when the age has arrived: when the lion lays down with the lamb; when no more wars occur ever again; when poverty and famine are historical blights and when all people recognize the G-d of the Jews/Hebrews as the one true G-d. So may it be during our lifetimes!