Should One Interpret Scripture?

Anytime I’m in a discussion with just about any Christian outside of Protestantism, the proof text of 2 Peter 1:20 comes up. The person, hearing my explanation of a passage, claims that my interpretation of the text is not valid by itself—I need the authority of the Magisterium or the Early Fathers or Something. But is that what the verse is teaching—that any interpretation of the text is dependent on the totality of the Church (be it the historical Church or the body of teaching from the Church) over (and against) the individual?