There has to be a connection between them. The athletics draw no resources from education, but how can this be so? Instead of increasing the budget of athletics, why can't the education budget be increased instead?
I went to UF. The athletic department is completely self-funded through donations, sponsorships, media rights deals, ticket sales, etc., and actually contributes about $5mm per year back to academics.
While that's true I don't think it is actually as compelling of an argument as it sounds on first blush.
I went to UF and I used to receive weekly emails asking for donations to the athletic program that I wasn't able to unsubscribe from without telling them that it was illegal to spam without any way of unsubscribing. I never to my memory got email asking for donations for anything educational.
A significant portion of alum just want to donate $X and it goes to the athletics department because of how the university is choosing to allocate it's fundraising, not because that is how individuals actually care to donate.
At some schools the athletics program gets considerable tuition revenue as well (in the form of a tacked-on "athletics fee"). UF seems to have one of the lower fees ($57/yr), though when multiplied by 50,000 students, that still works out to a bit under $3m/yr. It appears (see sibling comment) that athletics contributes back some surplus to academics, though, so may be a net positive at UF. Not true at all schools, some of which have much higher than $57/yr charges (e.g. UVA's $650).
Last I heard, LSU and Nebraska were the only two schools with athletic programs that were both financially and nominally self-sufficient. This was in 2009, I think. This link gives some financial stats on athletics programs starting with the 2004-2005 academic and ending with the 2009-2010 academic year.
In other words, the difference between the athletics budget and the academic budget represents the priorities of Americans in general, not any specific group such as a universities administrators.
Is that the case, or it sounds like from the other commentors here that it also represents the effectiveness and focus on fundraising? If instead people were given a single fundraising plea form with 2 checkboxes (one for academics, one for athletics) -- which way would most people go?