3 ideas
Disputants who start out seeking truth soon care more about not appearing wrong, because conceding a point wounds innate vanity. Once someone has committed to a position publicly, they will defend it even after privately seeing it is false. This works partly because a counterargument that occurs to them later might still rescue the point. Controversial dialectic therefore studies how to win, not how to be correct.
Every refutation takes one of two routes. It attacks the thesis either ad rem, by showing it conflicts with the facts, or ad hominem, by showing it conflicts with the opponent's own other admissions. Either route can be run directly against the premises or indirectly, by drawing out a false consequence or a counterexample. This map lets you locate exactly where any rebuttal, fair or foul, is operating.
One stratagem pushes the opponent's assertion beyond its natural limits and reads it in the most general sense possible, which makes it far easier to attack. At the same time you keep your own claim as narrow as possible. The broader a statement is made to be, the more exceptions it exposes. The defense is to restate the precise scope of what was actually claimed.