Jesus was a Jew both ethnically and religiously, he completed the religion by serving as the Christ whom the Scriptures long foretold even though majority of the Jews did not believe in him.
Christianity is the completed form of the Ancient Jewish religion, it is a pity that many of those who were ethnically Jewish did not recognize his role as Messiah, for this many did not accept Christianity, the completed form of Judaism. Instead they remained incomplete with the religion.
It wasn’t long before it was understood through the direction of the Holy Spirit that one did not need to be ethnically Jewish to be a follower of Christ, thus the Apostles began to preach to, and baptize many Gentile converts to the Christian faith. So Paul speaks about ethnical and religious Judaism :
“For he is not a real Jew who is one outwardly, nor is true circumcision something external and physical. He is a Jew who is one inwardly, and real circumcision is a matter of the heart, spiritual and not literal.” Romans 2:28-29
As time went on, unfortunately some Christians broke away from the Church founded by Christ, so that a name became necessary to distinguish one Church from another. It was later decided that, the Church Jesus founded be called “Universal” from Greek Kataholos which means “according to the whole”, this is how the term “Catholic” was applied to this Church.
So Jesus was a Jew to complete the Jewish religion by creating a Church that would fulfill it and be open to people everywhere irrespective of their tribe and culture.