Because the world revolves around legal technicalities.
Food for thought, the Big XII was not a continuation of the Big 8. That is despite the fact that it contained all 8 original schools. The fact is the 8 schools left the Big 8 and began a new conference. As did the Catholic 7. The main difference is that the Big 8 ceased to exist while the Big East didn’t. The Catholic 7 simply bought the name, but the American was and is the legal successor of the Big East. It even inherited the Big East’s BCS autobid for a single season before that was blown up.
Go to the wiki page for the Big East, and you’ll see a heading, “Original Big East (1979-2013)”. You’ll see that there because that is how the situation is viewed by the world at-large.
If Wake Forest, NC State, Duke, Virginia, Virginia Tech, Louisville, Georgia Tech all left and started a conference and bought the name ACC from the conference, it would be a new conference. Even with overlapping membership. And in future years, people could talk about remembering FSU dominating the old ACC and people would know exactly what was meant. If someone piped in and said “but FSU wasn’t in the old ACC“, they could both be accurate (FSU didn’t join for decades) and misleading (clearly FSU was in the old entity known as the ACC).
So while you are accurate that West Virginia was not a founding member of the Big East and therefore was not in the old BE circa 1980, West Virginia was clearly a member of the old conference once known as the Big East. Georgetown could say they were in both iterations of the Big East, but that doesn’t make the New Big East the same thing as the Old Big East.