The correct answer to this open question is the following.
The elements of centralization and formalization within the Arab Alliance and the IDF were key to understand the Israeli victory over the Arab army. Without a doubt, those inherent differences affected the outcome of the war.
The Arab Alliance was formed by soldiers from different Arab states such as Jordan, Syria, Saudi Arabia, Tunisia, Algeria, Morocco, and Egypt. The alliance had strong numbers, good supplies and weapons, machines, tanks, and the support of the Soviet Union.
However, the Israeli al Defense Force (IDF) won the war by capturing the Gaza Strip, the West Bank, and the Sinai Peninsula. And the Israelis could do that because they had better training, a different mentality, and a modern strategic approach.
Israel not only recruited loyal soldiers, as was the main cause for the Arabs. Israel recruited the best talent for each military position and trained until they became the best. Lack of this kind of recruiting and training was notorious in the Arab alliance.
Another factor that favored Israel was the Structure of Command and Control, emphasizing combat aspects such as strategy, swiftness, agility, improvisation, flexibility, and decision making on the move. Totally different from the bureaucratic Arab approach in the line of command.
That is why Israel won the Six-Day War that was fought from June 5-10, 1967.