Over on his Trinities blog, Dr. Dale Tuggy has a two-part podcast series that I highly recommend, 10 Apologists' Mistakes About the Trinity, wherein he exposes the more common fallacious arguments in favour of classical Trinitarianism:
10. The Trinity doctrine is not obviously contradictory, so problem solved!
9. There has always, or at least since the fourth century, been a single, dominant doctrine of the Trinity.
8. Trinitarian theology is obviously implied by scripture.
7. “The” Trinity doctrine is “the Christian view” about God.
6. Trite, new-fangled summaries of “the” doctrine.
5. New-fangled slogans and grandiose claims.
4. Dubious “proofs” of the Trinity from reason.
3. Flights of speculation about the atonement.
2. Confusing the Trinity with the “deity of Christ.”
1. Linguistic sophistry: “Let us make,” “elohim,” “echad.”
Part 1 (arguments 10-6)
Part 2 (arguments 5-1)
10. The Trinity doctrine is not obviously contradictory, so problem solved!
9. There has always, or at least since the fourth century, been a single, dominant doctrine of the Trinity.
8. Trinitarian theology is obviously implied by scripture.
7. “The” Trinity doctrine is “the Christian view” about God.
6. Trite, new-fangled summaries of “the” doctrine.
5. New-fangled slogans and grandiose claims.
4. Dubious “proofs” of the Trinity from reason.
3. Flights of speculation about the atonement.
2. Confusing the Trinity with the “deity of Christ.”
1. Linguistic sophistry: “Let us make,” “elohim,” “echad.”
Part 1 (arguments 10-6)
Part 2 (arguments 5-1)