In the light of the brain damage resulting from football, it is a serious question whether it's morally permissible to participate in or support the sport at all. Still, one can make a case that there are human excellences that this sport provides a particularly good opportunity for (I am grateful to Dan Johnson for this point), and the brain damage is an unintended side-effect, so there might be a defense of the sport in general on the basis of the Principle of Double Effect.
But I think it is particularly difficult to defend educational institutions supporting this sport among students. For the defining task of an educational institution is to develop the minds of the students. But brain damage harms the individual precisely in respect of mental functioning. And it is much harder for an organization to justify an activity that has among its side-effects serious harm to the goods pursuit of which defines the organization.