If Yeshua is the Messiah, then why don't the rabbis believe in him?

Some do!

Not all the rabbis, past and present, have rejected Yeshua (e.g., Orthodox rabbi Isaac Lichtenstein and Reform rabbi Dr. Max Wertheimer believed in Yeshua). If Yeshua is truly rejected by the rabbis, then he is in good company—the Old Testament (Tanakh) prophets were also rejected by the Hebrew people.

It was even predicted that Messiah would be rejected by his people (see Isaiah 53:3). Remember, the rabbis are human; they are not infallible. The final authority for the identity of the Messiah must rest with the Jewish Scriptures, and the first-hand witnesses, not with the rabbis. In fact, there have been enough rabbis that have believed in Yeshua that several books have been compiled with their stories.