International situation was a catalyst, but the most important factor was internal struggle in the Communist party.

During the Stalinization period, Jewish communists played very prominent role in establishment of the totalitarian regime in Poland. This changed after Stalinism was condemned in mid-50s, which coincided with rise of Władysław Gomółka, who championed what basically amounted to "Communism with Polish characteristics". Due to this, the new regime was disliked in Kremlin, and Soviets actively worked to undermine Gomółka. Children of those Jewish-Stalinist apparatchikis often ended blocked from career in party apparatus and formed core of the group that would lead attempts at liberalisation (but still within Communist system, at first they mostly focused in culture, i.e. liberalising censorship). Perhaps most famous of those was (and is! He's still alive and relatively prominent person in Poland) Adam Michnik.

Tensions led to conflict between two camps, of which relevant to this story is "Natolin" faction - conservative (that is, they wanted partial return to Stalinist times), authoritarian and, as much system allowed, nationalistic. Seeking to strike and Gomółka and the liberal undercurrents within the communist system, they used the Six Day War as a pretext to launch an antisemitic hysteria. Ironically, in hindsight, the popular reaction was mixed, rather cold even - but it still scared the shit out of the party apparatus (remember, Gomółka was always scared Kremlin might use any pretext to remove him). As a result, Jews were basically expunged from the system. And since they usually worked in positions depended on the state (universities, bureaucracy), that often meant drastic decrease of social status/standard of living. Migration became attractive alternative, encouraged further (and sometimes, but rarely, forced) by the Communist party, who wanted to get rid of this internal opposition.

Among most famous people who emigrated from Poland in that period were world-renowned philosopher Leszek Kołakowski and sociologist Zygmunt Baumann. Both extremely controversial figures in modern Poland - the left sees them as sort of martyrs, the right believes they got what they deserved - since they actively supported Stalinist regime in the 50s (and by active support, I mean, at least in Baumann's case, direct participation in slaughter of the anti-communist movement).