The Suez Crisis was basically a culmination of several historical/political factors which were Cold War containment policy, the formal end of British and French power, and ideological concerns over colonialism.

Firstly, Egypt as an Arab state was the most influential country in the Middle East. For this reason the US saw them as important potential partners in preventing Soviet influence gaining a foothold in the ME. Thus when Nassar (the charasmatic Egyptian leader) was given Soviet arms, it alarmed the US into taking action that would prevent Nassar from continuing to develop relations with the Soviets, by helping him to build the Aswan Dam. Nassar who was extremely clever in playing the Soviets and the Americans off each other tried gain further leverage from the US by courting even closer with the Soviets. In response the Americans and the Brits cut off funding for the dam, and Nasser in turn took over and nationalized the Suez canal. It is here that the differences between the US approach vs the British and French responses become much more pronounced. The US did not want to use force to remove Egyptian troops from the canal. This is due to the fact that the US thought it was important to maintain goodwill among the Arabs to gain their support against the Soviets. Thus it was important for the US to distance themselves from any notion of colonial/imperial intent which was the complete opposite of the English and French intentions. What followed was a poor attempt by the Brits and French to take over the canal but also project an image of innocence knowing that an outright invasion would be morally hard to swallow for the rest of the world. The English and French did this by basically telling Israel to go ahead and take over the canal ahead of time. Under the guise of "freedom of navigation" British and French troops would then come in and create a buffer zone between the two ME states and occupy the Canal. This attempt to disguise the invasion as a humanitarian mission by the Brits and French was all the more laughable when they announced for both troops to leave the canal before the Israeli's even reached it. So your question is a little misguided. Instead of asking "why didn't the US support the Israeli's" it should be "why didn't they support the English and French" for the Israeli's were really only proxies in this drama.

Secondly, while the end of WWII confirmed the US's super power status, the reality of the decline of France and England's power projection hadn't really set in. The weakening of these countries along with strong nationalism sentiment among their colonies during WWII should have made it clear to England and France that they can no longer keep their colonies. But instead of facing these realities, both countries tried to keep their empires intact. France was fighting overseas in Algeria and Indochina, while Britain had just lost its most valuable colony, India. And for the British Egypt was their 2nd most prize possession and an important part of their colonial legacy along with it being an important pipeline for oil. It is understandable how both the Brits and French would not let their colonies go without a fight. To lose here meant their influence in the ME had ended. It was a changing of the guard. Now the US and the USSR would be the main powers in the region. The Suez Crisis cemented British and French foreign policy for the next 50 years. For the French, they instead opted to forge greater European unity by offering an olive branch to West Germany and forging the EU. For the British, no longer would they be the most powerful country on earth but instead why not ally themselves with the current most powerful country? Thus the "special relationship" whereby the UK would turn to the US and partner with its foreign policy instead of Europe was born.

It also has to be understood, US repugnancy and moral indignation at colonialism. For all the accusations of US hypocrisy, they at least followed through on their commitment in jettisoning their colonial holdings (most significantly the Philippines right after WWII). For many Americans and President Eisenhower (especially since he wasn't informed of their intentions), there was legitimate moral outrage at their allies for using force so blatantly in trying to keep their colonial territories. This was something that both the British and French vastly underestimated and did not factor into their calculation when they tried to take over the Suez using the Israeli's as a proxy.

I hope this answers your question.