I guess different readers see things very differently, because I thought that McGonagall was a total badass in this chapter.

When someone makes a major mistake, based on an accumulation of errors from years of acting on a distorted version of their values, it takes a high-level rationalist and an impressive level of control and insight to be able to acknowledge their mistake, clearly see the values that were distorted, and set a new course that repudiates their old ways and appropriately takes their values into account. To be able to do that within a few hours, publicly, when they learned of their mistake through a vicious, personal, inappropriate chewing-out, seems like it might require one of those rumored double rationalists.

Or, if you must view it as a Harry vs. McGonagall conflict, McGonagall kicks his ass. In precisely the way that he needed to have his ass kicked.