Specifically Christian newcomers to the study of Judaism frequently puzzle over why — as they themselves often put it — Jews “don’t believe in Jesus.”
The reality is simply that the entire Jewish concept of who and what a Messiah actually is (or does) is just nothing like what Christians themselves have in mind, when they talk about Christ (meaning Jesus) as having been — or being — “the Messiah,” by which they mean a cosmic divine Savior, or a resurrected Son of God.
The Jewish concept of the Messiah, generally speaking, is of a mere mortal (not a divine being, not God incarnate, not God the Son incarnate, not a literal Son of God) who will be a political or military leader, rather than a spiritual or metaphysical “savior.” The Messiah is not conceived of, in Judaism, as someone who will die as a cosmic sacrifice in order to atone for the sins of all humanity, but simply as someone who will defeat Israel’s enemies, rebuild the Temple in Jerusalem, and establish a “Messianic Age” of lasting peace and justice.
The Jewish Messiah is in no way thought of as divine himself, nor as someone destined to die as a divine/human sacrifice and subsequently miraculously resurrected, nor as a Savior in whom one must place one’s faith and trust in order to receive his gift of eternal salvation. All of those are uniquely Christian ideas, not Jewish ones.
So, when at times some Christian newcomers to the study of Judaism puzzle over why Jews don’t believe that Jesus was (or is) the Messiah, part of their confusion may stem from perhaps not being fully cognizant of the fact that Jewish beliefs regarding the Messiah are simply not necessarily the same at all as Christian beliefs about the Messiah (or Christ). Perhaps without realizing it, they are looking at a Jewish concept with Christian eyes, or through Christian lenses, as it were.
What Christians have traditionally claimed about Jesus Christ for most of the past two millennia of Christianity’s history — that he is the Son of God or God the Son incarnate, that he is a resurrected divine Savior whose death made salvation available to all humankind, that faith in Christ makes for salvation, that salvation and eternal life are available through Christ alone — simply is not, and never was, part of the Jewish concept of the Messiah in the first place.
And apart from differences over just exactly what a Messiah really is, Jews additionally do not believe that Jesus could possibly have been the Messiah since, after all, Jesus simply did not accomplish what Jews believe the real Messiah will succeed in accomplishing. The Messiah, when he comes, will establish the Messianic Age, a lasting era of world peace and justice, a world and an era in which all will worship the God of Israel; obviously, this has not occurred.
Christians may argue that all of this will yet occur, when Jesus returns. But Jews do not believe that Jesus is going to return, because they don’t believe that Jesus was resurrected after his crucifixion. They don’t believe that Jesus was in any way divine, or the Son of God; they certainly don’t believe that Jesus was the incarnation of the second Person of a divine Trinity consisting of Father, Son, and Holy Spirit, because the theological concept of the Trinity is also a uniquely Christian belief, and not at all a Jewish one.
(Jews — and Muslims, too, for that matter — absolutely insist upon a staunch and uncompromising monotheism. To them, the Christian claim that God is One and yet somehow also Three smacks less of pure unadulterated monotheism, and more of a disguised “tri-theism.”)
And the many selected messianic verses found throughout the Hebrew Bible (or Old Testament) which many Christians cite as ancient Jewish prophecies allegedly predicting, anticipating, or otherwise referring quite specifically to Jesus Christ, are regarded by Jews as actually being nothing of the kind. Where many Christians see Jesus seemingly very clearly pointed to within such scriptural passages, Jews just as clearly see completely different meanings altogether. Jews read their scriptures with Jewish eyes or through Jewish lenses, whereas Christians read those very same scriptures with Christian eyes or through Christian lenses, and therefore their respective interpretations of those identical scriptural passages can and do vary widely (even wildly). As with the very concept of the Messiah itself, the differences here are also so great that it’s almost a case of “apples and oranges.”
And these are among the sorts of things that must be fully grasped, and appreciated, in order to begin to understand how and why Jews and Christians can have so much in common on the one hand (as sibling Abrahamic religions), and yet on the other hand differ so profoundly over certain absolutely core matters of their respective faiths.