The accusation of Israel waging an illegal, aggressive war has largely arose out of the post-war situation; in which Israel outraged much of the international community in the wake of their victory by taking quite a bit of land in the proclaimed interests of future defense. In particular, the Sinai; to form a buffer from further Egyptian aggression, the West-bank and Golan Heights - to create dominating salients from which to deny passage to Jordan and Syria, respectively.
However, from the perspective of Israel (and to some, International Law) , despite the Israeli air-operations against the Egyptians being described as a 'pre-emptive' strike, everything suggested that the coalition led by Egypt was about to wage aggressive war on Israel. While the mobilization of armed forces along a border is alarming in and of itself, it is rarely considered justification enough for a strike without further intelligence that suggests imminent attack or some other war-like act.
For the Israelis, said war-like act was the closure of the Straits of Tiran in June, 1967. In the late 1950s, it was decided that these Straits should remain open to all shipping from all nations. Closure of these straits would therefore provide pre-ordained justification for war. I quote:
a solution was seen in a French proposal that the maritime Powers announce in the General Assembly that all nations have the right to sail through the Straits of Tiran; the Powers would also recognize Israel's prerogative, under Article 51 of the United Nations Charter, to ensure this right against hostile interference.
Further on, the General Assembly outlines the purpose and scope of the UN presence in this area, which greatly resembled that of the Suez-zone. Both these areas of UN control would be swept aside by initial Egyptian moves in the high-strung run-up to the war.
The General Assembly's resolution (II) of 2 February 1957 contemplates that units of the United Nations Emergency Force will move into the Straits of Tiran area on Israel's withdrawal. It is generally recognized that the function of the United Nations Emergency Force in the Straits of Tiran area includes the prevention of belligerent acts.
^Ibid
The military reasons for the pre-emptive strike are far more straight forward compared to the political; the Israelis simply had no room to maneuver, save for forward. In order for the Israelis's to defend their small state, they would have to maneuver aggressively and defeat the enemy in detail (that is, one at a time if possible) before they could co-ordinate. To illustrate this, the political borders of 1967 Israel were narrow enough at some points that the distance between opposite sides of the country could be as small as 7 miles.