Step 1: Understanding the sentence meaning.
The speaker is hesitant to openly call the man a fraud, so instead they decide to attack the weaker parts of his theory. This suggests the second blank must mean “exposing errors.”
Step 2: Analyzing the options.
(A) denouncing – debunking: Denouncing means publicly accusing, and debunking means exposing falsehoods. This fits logically.
(B) ridiculing – proving: Proving does not fit the idea of attacking weak points.
(C) castigating – strengthening: Strengthening is opposite of the required meaning.
(D) mocking – destroying: Destroying is too extreme and does not fit the tone.
Step 3: Conclusion.
(A) correctly expresses hesitation to accuse directly and then exposing the flaws step by step.