Uhhh ... No. Rabbi and Priest are two separate things. Modern day Jews have Rabbis, who lead and teach the congregations. To be a Rabbi is not hereditary. There are no Jewish Priests today, because the Priesthood was hereditary, and genealogical records have been lost, and the name Cohen is not considered sufficient proof (although DNA testing may be used to restablish the Priesthood.) But Priests sacrifice; Rabbis teach. Not the same. Jesus was not a Levitical Priest, but He was a Priest after the order of Melchisadek.
It's a contradiction that all scholars of history recognize.
A little too sweeping. But Roman and Orthodox scholars have their own problems trying to identify Christian Elders (Presbyters) with Old Testament Priests. (The early Christians had had Elders, but no Priests.) This confusion is the cause of much misunderstanding.