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.
All I saw was somebody saying, hey, buddy, your church is only 40 years old, whereas mine is 2000.
You didn't say anything about tradition, but I admit to wandering into the middle of the discussion, so I guess I missed it.
Traditions, by the way, have been known to become incorrect and altered over time, for what it's worth.
