Aporia is professed doubt — the speaker declares that they do not know where to begin, which course to recommend, or how to express what they feel. The doubt is performed rather than real, and its function is to make what follows seem reluctant rather than rehearsed.
The figure buys sincerity, which is a currency arguments are otherwise poor at generating.
The classical form is a prosecutor opening by professing himself overwhelmed: so many charges, so little time, that he scarcely knows which to put first — before proceeding through all of them in a prepared order. The helplessness is the frame, not the condition.
Genuine aporia also exists: Socratic dialogues frequently end in real deadlock. The rhetorical figure imitates the posture of that deadlock without the substance.
Aporia works on the assumption that hesitation reads as honesty. A speaker who appears to be working something out in front of you seems less likely to be managing you than one who arrives with conclusions prepared, and audiences extend considerable latitude on that basis.
The device is therefore most powerful exactly where it is least warranted — in prepared, written, revised argument, where nothing is being worked out at all. A written aporia is always a performance, since the writer knew the answer before the sentence was finished.
That does not make it dishonest. Staging a difficulty can genuinely help a reader feel the weight of a problem before being handed its resolution. But the posture of uncertainty is doing persuasive work, and it is worth noticing when a passage's humility is a structural choice rather than a state of mind.
