Rhetoric is above (encompasses) logic because “argument” means to put together or construct properly. This is mathematical and relates to how we can usually “sense” a good argument from a bad.
What? That is counter-intuitive, you say? Only because you are thinking in terms of your “intuition” rather than in terms of your sense. Sophistry slides in-between these and co-opts your thinking toward apathy rather than toward properly constructed (beautiful/geometric) forms.
Logic as language is grammar and numerical operation. An atom obeys the same logic and speaks the same language as you do, but you happen to know a lot more words than the atom.
Argument has devolved to semantic games and emotional-psychological trickery. This is because you have lost your connection to your own heart. When you became convinced not to apply the rules of your own judgment, regardless of the outcome, you were separated from yourself and it became much easier for sophistic trickery to worm into your brain and supplant your natural rhetorical genius.
A good thinking process mirrors a good argument: it operates on sound principles and proceeds from clearly formed relations, toward integration (becoming more by combining in itself that which it finds, via the rules of synthesis of its nature). Eventually a good mind starts comparing and integrating its own rules of synthesis with those of the universe generally, namely a mind has begun to philosophize. Real philosophy is “putting together” the piece of oneself and of this existence into the most complex, intricate, derivative, subtle and beautiful designs. “Truth” is the guiding principle of the upright mind.
Bad thinking mirrors bad argument, namely it does not care about integration and its every move is geared toward preventing wider syntheses or deeper reconciliations. Bad thinking is a mathematical system akin to cell apoptosis or to a virus: it chops up incoming information according to arbitrary rules and ugly patterns until enough ‘chaos’ exists wherein that fragmentation it is able to embed and replicate itself, qua system and proces, anew. The guiding principle of bad thinking is “replication”, it is always trying to maintain a current state and to extend itself laterally across as much terrain as possible.
Of note here is also how this reveals the deep structural flaw in the “Nietzschean”-esque mentality so common to internet philosophizing: the idea of “strength vs. weakness” is one of the most effective tools available to the viral mind to assist with its chopping-up of incoming data into smaller, more disconnected, fragmented and arbitrary bits.