The Six-Day War between Israel and its neighbors Jordan, Syria, and Egypt was a conflict that the United States chose to stay out of, despite Israel’s entreaties for military support. Egypt and Syria were Soviet allies at odds with American-aligned Israel. The local conflict could easily have turned into a direct conflict between the superpowers, which neither the United States nor the USSR wanted. The countries directly involved were left to fend for themselves in what proved to be an overwhelming military and territorial victory for Israel — one that doubled the fledgling country’s size in less than a week.

This is factually wrong. Fuckin' Nasser founded the Non-aligned movement:

The Non-Aligned Movement as an organization was founded in Brioni, Yugoslavia in 1956, and was formalized by signing the Declaration of Brijuni on July 19th, 1956. The Declaration was signed by Yugoslavia's president, Josip Broz Tito, India's first prime minister Jawaharlal Nehru and Egypt's second president, Gamal Abdel Nasser. One of the quotations within the Declaration is "Peace can not be achieved with separation, but the aspiration towards collective security in global terms and expansion of freedom, as well as terminating the domination of one country over another". The Movement advocates a middle course for states in the developing world between the Western and Eastern Blocs during the Cold War. The phrase itself was first used to represent the doctrine by Indian diplomat V. K. Krishna Menon in 1953, at the United Nations.

Syria and Jordan signed in '64. You have three member countries of a bloc deliberately assembled to counterbalance NATO and the Warsaw Pact fighting a defensive action against a rogue nation that attempted to invade the Suez (with NATO members England and France) thirteen years previously. That invasion was SHUT DOWN by the United States:

The three allies had attained a number of their military objectives, but the Canal was now useless and heavy political pressure from the United States and the USSR led to a withdrawal. U.S. President Dwight D. Eisenhower had strongly warned Britain not to invade; he now threatened serious damage to the British financial system by selling the US government's pound sterling bonds. Historians conclude the crisis "signified the end of Great Britain's role as one of the world's major powers". The Suez Canal was closed from October 1956 until March 1957. Israel fulfilled some of its objectives, such as attaining freedom of navigation through the Straits of Tiran.

As a result of the conflict, the United Nations created the UNEF Peacekeepers to police the Egyptian–Israeli border, British Prime Minister Anthony Eden resigned, Canadian Minister of External Affairs Lester Pearson won the Nobel Peace Prize, and the USSR may have been emboldened to invade Hungary.

The Six Day War was Israel attempting to prove it was a regional power against the Non-Aligned movement embodied in pretty much every Sunni neighbor they had. The Liberty was the US keeping SIGINT tabs on the whole mess and no surprise, the Israelis viewed the US as hostile. Remember - at the time, our staunchest ally in the Middle East was Iran.

The fact that we gave Israel absolutely zero heads-up about the massing troops preparing to annihilate Israel in the Yom Kippur War of 1973 was no doubt retaliation for the Suez Crisis and the Six Day War, and led to the environment that allowed the Camp David Accords, which were followed by the Iranian Revolution, which were followed by the proxy war of Iran against Israel via Hamas and Hezbollah in Lebanon, which led to US Marines being blown to shit by Iranians, which pretty much cemented us as aligned with Israel for the past 40 years but at the time of the Liberty? They were not our friends.

"Hey, remember that time the Israelis fired on us in open warfare? Yeah, prolly oughtta keep wraps on that, especially considering that ship didn't officially belong to the CIA." It's about that simple, and not at all surprising given the complex political environment surrounding South Asia that this shit is still classified.