Since when do claims of antiquity help one determine who is right?
If that is the case, the Jews of 2000 years ago had every right to point at the new followers of Jesus and tell them they were a bunch of upstarts.
You tend to oversimplification. It is not merely a "claim of antiquity." It is a claim of tradition built from the time that Christ named Peter as the first head of His Church: St. Peter, the first Pope.
The Jews were God's chosen people. We hold the Old Testament in great reverence and much of our Liturgy is drawn from it. That the Jews chose not to accept Christ as the Messiah is understandable. There have been many religions that have since broken away from the Catholic Church. You make your choice and you stand by it.