Harvard University is a corporation.

As a collection of people, entitled to First Amendment protections of speech and to the power of religious discrimination, according to the Citizens United and Hobby Lobby decisions.

So why is it that Harvard University was not allowed to admit into its halls people of its own choosing? Do I not as a person have freedom of association? Do I not have the First Amendment right to choose who I will and won't admit into my home? Did not the Citizens United and Hobby Lobby cases affirm/extend those people protections to corporations?

And why didn't Harvard's lawyers argue that angle in front of the Court?