The selection in which the sentence is properly puntuated is D) My sister and I recognized and identified the flaws in the man's argument, but we couldn't put our objections to words.
This is the correct option because it is necessary to put a comma before the subordinating conjunction "but" since, in this case, it is separating two independent clauses ("My sister and I recognized and identifies the flaws in the man's argument" and "We couldn't put our objections to words"). They function as two independent clauses because they could stand alone as complete sentences. Furthermore, the comma before "but" is the only one that is necessary; therefore, all the other options are incorrect.