If a leader/manager who completed their MBA at Harvard, but acts like complete arrogant jackass at work, doesn’t this mean the “best education“ failed them?

Not sure whether this is the right sub for this but had a thought… I don’t know what the curriculum is in Harvard’s MBA program, but I assume “leadership” has to be part of it? I have worked with people who did the program and are the leaders of the org – they were pretentious and arrogant. This attitude causes a decline in productivity for the team. Now, I’m sure not all of them are like this, but if someone had a Harvard MBA education, and still cannot lead a team effectively, isn’t that proof that the education they paid $$$ for failed them?