In the words of the Ivy League office, "We believe that our student athletes should aspire to achieve excellence. However, we feel that postseason play in football is not consistent with these values. We want to keep the focus on the student part of the phrase 'Student Athlete', and thus, postseason football does not put focus on the 'student' part, but rather the 'athlete' part"
That's a rough paraphrase, but in short, the league feels it isn't consistent with the idea behind the founding of the league. Sucks too, because there have been some really good teams that played in the Ancient Eight.
(FYI, I root for the Ivy League in general, although I find myself going for Harvard and Princeton more out of the bunch though)