Also, isn't Jesus technically a Levite, not a Jew? Since His was a virgin birth, thereby making Mary's genealogy the only relevant genealogy with regard to His actual lineage, and though I'm not sure it's necessary settled and certain, it's probable that Mary was a Levite (i.e. from the tribe of Levi). Joseph was from the tribe of Judah, but Joseph technically had nothing to do with Jesus' conception, so biologically speaking, his lineage is irrelevant to Jesus' lineage.

It seems Jesus is only called a Jew because Joseph was a probably a Jew, and legally, paternal lineage was all that mattered at the time, while maternal lineage was largely disregarded. And this is an especially tricky situation here, too, because you have to accept the virgin birth, which many Jews were not willing to do.