Mine would be, the fact that Kentucky is the ONLY school ever. To have 5 different head coaches win national championships..... And if you want to take this a step farther. I'm sure that UK is the ONLY school ever. To have 6 different head coaches to advance to the Elite 8. And not only that, but to also win 30 or more games in a season.
It isn't actually one thing but I can spin it as such. Preponderance of evidence.
It is the consistency of being elite over decades and different coaches.
It's the number of championships with all those different coaches.
It's the all time wins and winning percentage.
It's our fans taking over gyms all over creation.
It's all the Final Fours.
It's all those conference championships.
It's a huge pile of Sweet 16's and a ton of regional finals.
It's all the great players.
It's tens of thousands game in game out more consistently than anyone.
It's all the classic games throughout college basketball history wins and losses.
It is all the different forms of excellence that combine and pile up to make Kentucky Basketball the flagship program in college basketball, any single item is subject to change and jockeying but it is the overwhelming point by point case that can't be really argued or easily bested even over a number of years.
All other arguments are one note and easily refuted to my mind.
No sane person would switch places with any program, in my opinion.