Dr. Teeth,
Now for the 1967 war. After the 1956 war UN troops were put on the Israeli-Egyptian border to prevent raids. This was not the case though with Syria and Jordan. For years Syrian Artillery would pound Israely towns from the Golan Heights with Israel unable to do much about it given the entrenched and defensable terrain of the Heights. In addition to the raids, the Israely's suffered many Civilian deaths from from Syrian artillery from the Golan.
In May of 1967, Syria, Jordan, and Egypt mobilized their armies. Many in Israel thought this was just a scare tactic and did not take it seriously until Egypt forced out the UN observers from the border. The Egyptians then again closed the Gulf of Aqaba to Israeli ships.
Faced witht the possiblity of a 3 front war, being heavily outnumbered, some points along the then Jordanian-Israely border being only 10 miles from the sea making it possible for Arab forces to easily cut the country in half, artillery bombardment on Israely citizens from Golan and raids from both Syria and Jordan, Israel on June 5, 1967 launched a daring pre-emptive airstrike that was successful in destroying the Egyptian, Syrian and Jordanian Airforces. Israel was thin able to concentrate its forces more on Egypt and Jordan while leaving only a small defensive force to block Syria. This allowed the defeat the Egyptians and Jordanians and then concentrate on Syria.
Attacking the Golan Heights was a difficult task for Israely forces, but they were successful and it has to this day prevented Syrian Artillery from pounding Israely towns.
If Israel had not taken these actions it could have very easily been wipped from the face of the earth. First Arab forces greatly outnumbered those of Israel. Second the quality of equipment used was roughly the same. Israel was still using M4-Sherman tanks in 1967! A tank that was at best of average quality during World War II. The Arabs were armed with Soviet made T-54 tanks and older Soviet T-34 tanks. Both were either a match or superior to anything the Israelies had. 3rd, Jordanian and Syrian forces were fighting from higher ground, always an advantage in war. Cutting of and encircling Israely forces would be easier than falling off a log, given the geographic situation for Israel vs its neighbors.
What saved the day was Israel pre-emptive strike, plus Israely brains vs. how should I say, some really bad and uncoordinated moves by the Arab political/military forces. Clearly the Arabs could have destroyed Israel without swift action by its forces.