I don't remember the media being particularly against the Korean War. A certain percentage of the public was ambivalent, or worse, about it because they couldn't see how it was in our national interests and because the memories of WW II were still so fresh.
But the virulent blame-America-first , anti-war movement really was born when the Baby-Bopomers reached draft age.
They thought they were too important to get their asses shot off.
The inflation of BA degrees rendered the Baccalaureate degree to the former level of a High School Diploma.
Universities welcomed the influx of funds, and those who taught the new horde of 'social scientists' welcomed the increase in prestige and grant money which came soon after.
Naturally, one of the purposes of study is to promote further study, especially when endowments are involved.
Much of the psychobabble and social serpent-speak heavily interlaced with the liberal antiwar, antigun, anticonflict, criminal mollycoddling mindset comes out of this era.
Although this is a bad enough result, the deferment turned the Universities into a hotbed of antiwar activity, and Liberal domination of many Universities' curricula really came into its own; a philosophical paradox, considering the capitalist nature of those who ultimately funded through tuition and fees much of this change.
Perhaps, if in the future, our nation finds itself in the position of reinstating the draft, the deferment can be limited to fields essential to the national security or of strategic importance. That might swing the pendulum back.
Had those who protested served, things might have been different. I am just not sure I would want them to cover my back when the chips were down.