In Pete Seeger's own words:

[1998:] In October, 1955, I was on a plane bound for Ohio - half dozing. I found in my pocket three lines copied a year before when I was reading, And Quiet Flows the Don, the Soviet novel by Mikhail Sholokhov, who describes the Cossack soldiers singing as they galloped off to join the Tzar's army. 'Where are the flowers? The girls have plucked them. Where are the girls? They've taken husbands. Where are the men? They're all in the army.' Something clicked in my subconscious; I remembered the phrase I'd thought of a couple years earlier, 'long time passing', a singable three words. Then, I added the handwringer's personal complaint, 'When will they ever learn?'Twenty minutes later, it was completed. I recorded it for Folkways in 1956 with several other short songs. A year later, I stopped singing it, thinking it another not-too-successful attempt. But Joe Hickerson, leader of the Oberlin College Folksong Club, picked it up and added two verses. He gave the song rhythm. The Kingston Trio and Peter, Paul and Mary eventually picked it up, too. (Notes 'Where Have All the Flowers Gone - The Songs of Pete Seeger')

He also says - in the book of the same title, I think - that he thinks the German version superior to his own. It was written by Max Colpet (not Coplet!), a German Jewish author and songwriter (see Wikipedia).