Catholics don't follow the non-Catholic Rule of Faith. Catholics would look to the Magesterium for doctrine, not to the Bible per se.

The Catholic Rule of Faith is Scripture + Tradition, which cannot contradict each other.

Catholics believe Jesus gave us a church initially, not a Bible. The Bible came later through His Church.

The Protestant (non-Catholic Christian) Rule of Faith is sola scriptura. Yet even that teaching itself (sola scriptura) cannot be found anywhere in scripture.

In sum, it's a different ecclesiology.