Was the justification of the 6 day war propaganda? Or were Egypt, Syria and Jordan actually preparing to invade. If the former, how was it so successful that it is the accepted narrative around the world today?

In May of 1967, Egypt expelled the UN peacekeepers stationed in the Sinai since the Suez Crisis and moved Egyptian forces in. That same month, he blocked Israel's access to the Red Sea by closing the Straits of Tiran. The latter was Israel's justification for participating in the Suez Crisis, so Nasser must have known that he was baiting Israel at that point. Egypt and Syria were already very close and coordinating. In the same month, Jordan signed a military alliance with Egypt and Syria, which guaranteed their involvement. In addition, Iraq, Kuwait, Sudan, and Algeria began mobilizing their military forces. In general, Egypt, especially under Nasser, was seen as the leader of most of the Arab world. His actions leading up to the Six Day War spurred other nations to follow his lead, which led to military mobilizations in many Arab states, including three bordering Israel, which prompted Israel's preemptive strike that basically guaranteed them victory.

There is blame to be given to both sides of most wars that have occurred, but the immediate causes of the Six Day War reside with Egypt.