Simply mobilizing along the borders, but not firing a shot, is EFFECTIVELY starting a war with Israel.
Israel has a far smaller population than the neighboring Arab states, and thus has to mobilize a far higher % of its population for war. The Israelis are unable to mobilize their entire army and keep it mobilized for more than a few weeks, maybe a month, before their entire economy would collapse because there's no work getting done. However, the Arab states can stay mobilized far longer. So, basically, Israel generally HAS to strike first; they can't sit around mobilized forever.
In 1967, technically, the Israelis "started" the war because they fired the first shots; The reality was that they really couldn't do much else.
The Arab states are aware they'll get struck preemptively if they even begin to mobilize in a serious way; hence, they don't do so.
They wiped out the entire Egyptian Air Force, bombs loaded, on the ground just as they were gassing up and heading to combat. The Mosad knew their flight plan. Good intel wins wars, and in an area as compact as that, it pays to have a hair trigger.
In 1967, the Arabs "technically" started the war by blockading an international waterway to Israeli shipping (a recognized act of war). The Jordanians were even more "technical" by firing the first shots at their armistice lines with Israel.