The scriptures speak with God's authority

This scenario often plays out; two Christians will be debating doctrine, one of them will appeal to God's word, the other will ask "are you God?" and insist that it's not God they're disagreeing with, it's the other Christian's interpretation of the Scriptures. Moses faced a similar challenge in his day. Korah, Dathan and Abiram argued with him, insisting they were holy too, so how could Moses claim to have some special authority?

It would be foolish to compare the two scenarios exactly. A Christian with correct doctrine is not speaking with authority, neither does the Lord perform miracles to verify who is correct. However, while we are not prophets ourselves, we do have the words they were inspired to write. It's not a case of we both serve God differently, it's a case of the Bible says something, therefore it is true.

What gave Moses his authority? The word of God. What gives a Christian his or her authority? The word of God. When you stand firmly on the word of God, you don't have authority, neither do you need authority. The authority is the word of God. All you're doing is standing firmly on it. This may not give you the right to tear through the earth and cast a heretic into its center, it does mean you are defended from the heretic's error. And yes, you absolutely have the right to call them out on those errors.