Pro: Having a successful "big time" athletic program gives the university valuable national exposure that it wouldn't get otherwise.
This is the "Everybody Knows O.J." argument.
The logical error is a failure to distinguish between "exposure" in the sense of mere name recognition -- which can be a very bad thing -- and something like "earned prestige" or "deserved reputation."
Mere "exposure" is worthless. One of the most-discussed events of recent years was the O.J. Simpson trial. Those whose "name recognition" increased as a result do not seem to us models to be envied or imitated.
On the other side, "reputation" very often comes not from "exposure" but from a long-term commitment to genuine intellectual attainment.
At the institutional level, for instance, Harvard enjoys a reputation as a good university. Not because it has a winning football team, but because it has remained committed to academic and intellectual values over a long period.
The bottom line: the exposure Rutgers might get from football or basketball is simply "O.J. recognition" given to any name splashed across a TV screen with some frequency. Such "exposure" is in itself valueless.
The "reputation" Rutgers stands to achieve by abolishing professionalized sports and devoting its resources to intellectual and artistic accomplishment would be, on the other hand, immensely valuable. ( Source: Gerdy, Ch. 4: "Does Athletics Generate Positive Visibility?")