You want to be with your peers. In our case that is land grant universities, not small Catholic private schools. Our interests simply would not ever align particularly well.
There is def some truth here, but there may be more nuance to small / private / catholic than many might think.
Butler is small and private, but not Catholic. The Big East is already not all Catholic (although it is all private).
Small Private Schools that are competitive P5 - Notre Dame, Boston College, Stanford, TCU, Vandy, Duke, Wake, Northwestern. They are all under 10,000 undergrad.
P5 Private Schools that are a little larger - Miami, Syracuse, USC, Baylor.
A Peers definition should be more than "Land Grant". Think Florida A&M, Alaska/Fairbanks, Maine, MIT, Alcorn State, etc.
Peers can also consider geographical region, academics, sports offered, history and rivalries, etc.
St Johns, Villanova, and Georgetown may be have more peer comparisons to UConn in some's view than Alcorn State or Maine.
If you don't want to have private or Catholic schools as peers, than the ACC is probably not a fit either.