"Thus, why should we assume that any attempt to block the military from recruiting on college campuses is a violation of the military's or student's freedoms to associate with or access one another? If the military bans me as a peace activist from entering its academies, boot camps, and regiments, why can't universities do the same? If the democratic will of the university community decides that military recruiters are not necessarily in line with the university's goals, then the school should be able to exercise its freedom of association and ban recruiter access, just as the military does with all other organizations."

Because a university and the military are not at all the same.

And a school can exercise its right to ban recruiters - it just does so at the peril of federal funding. Similar to how the federal government tied highway funding and their desire for a universal 21+ drinking age together.