We know the teaching was faithfully handed down because we have the promise of Christ that the Church he founded and entrusted to his apostles would teach faithfully and with authority.
A better question is this: why do Protestants believe the Bible is trustworthy? Seriously — why? How do they do that without relying on the authority and tradition they claim to reject? How do they live with this level of denial and incoherence?
boatbums has answered that question in the past far better than I can.
Most of Scripture was recognized as such by the people in those days. Jesus quoted from virtually all the OT, verifying and validating it.
Peter called Paul’s writings Scripture, validating it as well.
What was recognized as Scripture was recognized as such before the Catholic church came into existence.
The issue isn’t about Scripture either, as it is written down and people can go back to it and read it themselves. It is a great means of keeping something from changing over the years as it is passed on. People can go back to the oldest original manuscripts if there is contention about exactly what was said.
The same cannot be said of oral tradition. Word of mouth is inherently and notoriously unreliable. All the claims of God’’s promise that He’d protect those oral traditions are made by those same people who claim to have them. There’s a conflict of interest right there. There’s simply no way to objectively substantiate that claim.