Why would these elite schools want to maintain their privilege to turn away female applicants for sexist reasons? Well, for sexist reasons obviously. Ivy Leagues believed that educating women was generally a waste of time and resources (again, this was the nineteen seventies, not the seventeen seventies) as they were only getting their "Mrs. degrees" to shop around for husbands and be slightly more interesting during cocktail parties. And since private universities consider themselves the purveyors of the finest, most exclusive education on the continent, it was their academic duty to turn away these useless women in favor of accepting as many future tobacco company VPs as they could.
Sure, that attitude may have been totally out of sight, daddy-o, back in the seventies, but private universities still cling to their exemption to this very woke day. Ironically, that's in part because Title IX did change one thing about the Ivy League admissions process: Half a century of not being discriminated against has made the number of worthy female applicants soar sky high. If they'd now have to admit both genders at the same, fair, rate the number of male students would drop to barely 40%. So in perhaps the utter worst example of affirmative action, Ivies now keep their finger on the scale for young rich men, artificially maintaining the ratio at 50-50.
Of course, modern faculties don't discriminate against their female students on the same misogynist grounds as the days of disco -- they've picked a brand new one. A 60% female student body is what admission admins fear is a kind of tipping point where people perceive you not as a regular college but as a 'women's college.' And that reputation makes you less popular with the private universities' most desired type of applicant: dumb rich dudes from dumb rich families whose dumb rich dads won't pay for an extra library wing just to have their sons attend some a pseudo-Sarah Lawrence College. Ironically, having way more women than men is believed to also cause a drop in application rates from female students, who too believe that attending predominantly female colleges won't look good on their future resume. So congratulations, Ivy League, you successfully taught entire generations that too many smart women in the same room is a bad thing.