John McCain has an op-ed in USA Today explaining why he is opposing Elena Kagan:
In 1987, I had my first opportunity to provide "advice and consent" on a Supreme Court nominee. At that time, I stated that the qualifications essential for evaluating a nominee for the bench included "integrity, character, legal competence and ability, experience, and philosophy and judicial temperament." On that test, Elena Kagan fails.
When Kagan was dean of Harvard Law School, she unmistakably discouraged Harvard students from considering a career in the military — even while claiming to do otherwise — by denying military recruiters the same access to Harvard students that was granted to white-shoe law firms. Kagan did so because she believed the military's "don't ask, don't tell" policy to be "a profound wrong — a moral injustice of the first order."
While Kagan is entitled to her opinion, she was not entitled to ignore the law that requires universities to allow military recruiters on campus under terms of equal access with all other recruiters. The chief of recruiting for the Air Force's Judge Advocate General Corps described the impact of Kagan's changes by saying that "Harvard is playing games." The Army's report from that same period was even more blunt, stating, "The Army was stonewalled at Harvard."