This is an interesting set of passages -- not that they aren't all, in the Phenomenology!
I need to point out that there's a small error at the start of this video -- the very first slide has the previous lecture's (54-55) numbers rather than the present one. But rest assured, this is indeed paragraphs 56, 57, and 58
One of the key things to look out for here is a new target of Hegel's critique of other, prevalent, but deficient modes of philosophical thinking -- what he calls Räsonieren, translated in Miller by "argumentation", "argumentative thinking", or "ratiocination". This is the sort of approach that he will later discuss in terms of "skepticism" -- a use of human freedom towards whatever content is being developed or discussed to simply say "no" to it, by means of use of the understanding, though critique, analysis, argument. . . .