What do I say to someone who claims Tradition as his reason for rejecting the Church’s authority?

Point out that his claim about “clinging to Tradition” is precisely what is claimed by all schismatics–Orthodox, Donatists, even, in their own way, Protestants, who say they believe only what was “handed down” by the apostles in Scripture. Everybody says that what they are clinging to (as against Rome) is “Tradition.”

But when you ask these various factions how they know that their views rather than Rome’s represent the true Tradition, they all fall back on private judgment: “Look how this Romanist practice or decree contradicts this earlier council or text of Scripture! Clearly our view–not Rome’s–represents Tradition (or biblical teaching).”

In practice, schismatics do not receive their Church’s teaching on their church’s authority; they accept their church’s authority because they agree with their preferred teaching. They don’t accept the message at the word of the Messenger, they choose the Messenger based on the message.

Ask your friend who is the arbiter of what does or does not constitute sacred Tradition: the individual, or the magisterium? Either the Church is our judge, or we are its judge. Either we judge our ideas by the teaching of the Church, or we judge the teaching of the Church by our ideas. And that includes our ideas about Tradition.