Bishop Williamson understood the root theological / philosophical causes of Vatican II better than any prominent Traditional Catholic leader out there, better than even Archbishop Lefebvre.
He traced the root causes much farther back than anyone else from among the mainstream Trad clergy, most of whom imagined that things were great through the 1950s, after which there happened some inexplicable, sudden, dramatic collapse that "came out of nowhere".
He recognized that the root cause of all the errors in Vatican II was subjectivism. No one else picked up on this, focusing instead on the individual errors than on the root cause. It's like doctors who treat the symptoms vs. the very few who try to identify and treat the root cause of the symptoms. He recognized how this started in the "Renaissance" and "Enlightenment" (which he correctly identified as really a re-death and a darkening of minds), tracing this trend through the philosophers, and ultimately the phenomenologists.
So that is THE most powerful teaching I received from him ... to the point that I take it much farther now than even Bishop Williamson, recognizing that the subjectivism in terms of entering Catholic theology started with the undermining of EENS in the early 16th century. I see the nexus between the philosophical trends and the theological trends at EENS dogma, the touchpoint between the rise of subjectivism and its infection of Catholic theology. But I won't digress too much.
That is by far the most powerful thing I was taught by Bishop Williamson in terms of philosophy and theology, and it has completely changed the way I think.
See, by identifying the root cause of these errors, Bishop Williamson helped protect us from other manifestations of error from this same root caause in the future, rather than many others who just played whack-a-mole with this particular error or that other error, treating this symptom or that symptom, unable to get a handle on it due to not understanding the root cause, and even often succuмbing themselves to some errors, since, again, they were not equipped intellectually to recognize the error for what it is.
Bishop Williamson didn't just hand us fish, but he taught us HOW to fish. He taught us HOW to think and reason, rather than merely regurgitate why this or that specific error is wrong.
Bishop Williamson also hammered into my brain that "ideas matter", that they matter more than anything else. So, the modern world has gotten to a point where as long as we "get along" and are "nithe", it's OK if we have different core principles, and we can just hold hands and sing "kumbaya" together, and then go sit around on our own to think thinks without any consequence, that ideas, i.e. philosophy, was merely an abstract exercise done for entertainment purposes.
And he was also right about certain historical issues that have corrupted politics for going on a century now.
God bless Bishop Williamson.