It was NOT a new movement. Many of the schools had attempted or flirted with doing so long before WW2.

The Harvard Faculty and President Charles Elliot had campaigned for years to ban the playing of football in the 1890s, and had also tried to ban the curve ball pitch when he learned it was based on deceiving the batter.

Columbia and Cornell had both dropped the sport at times before the 1905 formation of the NCAA.

Then with the explosion of numbers in colleges on the GI Bill, it meant that in the era before scholarship limits the big boys could simply pay for larger teams than anyone else to help them win.

Thus many schools not just the Ivies shied away from the expanding costs, and thus you have NCAA reforms for limited roster numbers and expenses, and then in 1976 the split between NCAA Division IA and IAA in football.

But it is also not fair to say the league "Abandoned" athletics, they still play a total of 33 sports as a conference and indeed was only formalized as a conference in the mid 50's, play outside schools, and award conference championships, and even still participats in many NCAA championships such as the Men's and Women's Basketball tourneys.

They are also not the only schools to no longer offer direct athletic scholarships, Georgetown for instance also does not for its football team.

So in short you have the traditional concern at many of the Ivies dating back to the start of college sports about the potential commercialization and corrupting influence, and the looming spending competition and differences between the haves and have nots meant the Ivies decided almost to head it off and take themselves out of the fight amongst themselves to avoid a runaway arms race nobody would win.