When we look at the Suez Crisis, we should perhaps understand it through the context, the event and the resolution.
Context
By 1956, the United Nations was an available platform for sovereign states to negotiate, mediate and engage in diplomatic discussion. Abiding by the UN Charter, Article 1(1) importantly declares that the UN was to maintain international peace and security, which is then enforced by the UN Security Council. The permanent members of the UNSC, also the most eminent, the P5, had included US, France, Britain and USSR (and China, who was irrelevant in the Suez Crisis).
On the other hand, the Cold War waged between the USSR and US often influenced the actions of both superpowers, who sought to shape international events to their interests in order to gain an advantage over the other, as seen from (very importantly) the Korean War. Both superpowers would most definitely work against each other if the event served to benefit them in the Cold War competition in the long run. In the case of the Suez Crisis, however, it had less of a strategic significance or bearing in relation to the Cold War rivalry, considering that Egypt was part of the Non-Aligned Movement, who had declared in 1955 to be neutral and not take sides in the Cold War - meaning the safety of Egypt had little benefit to either the US or USSR gaining an edge in the Cold War, since the globalisation of the Cold War was very much based on the principle of gaining a global alliance, i.e. drawing in other international states to their side, and Egypt firmly refuses to do so. Given this, upon the occurrence of the actual crisis, the US and USSR would view this as an issue of multilateral sovereignty dispute as opposed to a Cold War conflict.
Event & Resolution
The issue with the Suez Crisis was that France and Britain had been the instigators of the conflict, landing troops and seizing control of the Suez Canal. Since these two states are part of the P5 within the UNSC, they had ironically violated the very UN Charter they were meant to uphold. One of the violations was to Article 2(4), which essentially calls for the refrain of the use of force against the territorial integrity of any state, and this was recognised by the US - Eisenhower, the US president at the time, had pointed this out (around 2:37 in this video) in a speech. Given that the event would not matter in the scope of the Cold War, the US and USSR then treated this as a matter of international dispute that they had a responsibility to resolve in the context of the UN, which was founded exactly to find a solution for these international conflicts. As a result, there were no real sides taken in the Suez Crisis, since the US was simply operating to fulfil the responsibilities of the UN to uphold international peace and security, through forcing the Anglo-French-Israeli coalition to withdraw from Egypt. While France and Britain may still exist individually as US' strong bilateral allies, the US was more obligated to take a stand against them to fulfil the responsibilities of the UN. Similarly, the US could sideline its rivalry with the USSR and instead work to solve the most immediate dispute at hand, while the Cold War rivalry was merely latent, and again, had little influence in this crisis.
Attempting to work through the UN, the initial resolutions to call for withdrawal was naturally vetoed by the Anglo-French. Ultimately, the invaders were persuaded to relent through Resolution 118, later allowing the UNEF I peacekeeping force to be formed and sent in to Egypt to supervise the withdrawal and keeping peace for the next decade, resolving the conflict. The caveat for the end of the conflict was that the USSR refused to contribute to the over $200 million operational expenses of the UNEF I, which reaffirmed the idea that no firm sides were taken in this conflict, as USSR undermined the financial stability of the UN by doing so. (Later, the cost of UNEF I was covered by voluntary contributions from other UN states.) The USSR and the US had not actively worked together, as US had, for a large part, unilaterally drove the forced agreement of the British to withdraw through placing an oil embargo on Britain in 1956 and later threaten to influence the IMF to deny a loan to Britain should she persist. Suez Crisis' resolution was hence achieved largely through the US' insistence on upholding the principles of the UN, treating their allies as no-strings-attached disputants within a sovereignty dispute and, fortunately, without the burden of the Cold War upon it, which allowed the USSR to be a temporary ally. Overall, the Suez Crisis is a rather prominent case study in respect to the United Nations' Cold War peacekeeping, and a rare example of an UN success.
Sources:
Roberts, A. & Kingsbury, B. (1994). United Nations, Divided World: The UN’s Roles in International Relations . : Oxford University Press.
Thomas g weiss, David p forsythe & Roger a coate (2013). The United Nations and Changing World Politics . : Westview Press.
I have to be honest, the other answer in this thread talks about the notions of international law and fairness, but ignores the actual decisionmakers who chose to side with the USSR. Doing that provides a nice narrative about how the UN theoretically works and how international law sets expectations. Unfortunately, it's not really what many of the decisionmakers in the US government were paying attention to. I've heard plenty of explanations for the Eisenhower administration's actions during the Crisis, but few focus on "UN success", mostly because it's not viewed as a serious UN success for peacekeeping. In fact, some argue that the UN's failures are what helped cause the Suez Crisis in the first place.
I'll also note the other answer makes some strange historical mistakes. It claims that Resolution 118 was persuasive in ending the Crisis. However, UNSCR 118 was passed on October 13. The Crisis began on October 29. UNEF was created through the General Assembly, but only after the withdrawal was agreed to, and not through Resolution 118 or the Security Council, so it seems impossible to argue that this somehow demonstrated a UN success. I discuss other irregularities in the other answer below.
First, the context: Until at least 1955, the Eisenhower administration (in place since 1953) was far more friendly to Egypt than the British or French, who were wary of Nasser. In fact, the British often regarded the US's positions as a betrayal of the Anglo-American alliance, and took countermeasures to needle Eisenhower. One classic example is the case of British withdrawal from the Canal Zone. The British were unhappy with proposals for negotiations with the Americans as a mediator, and expected the Americans to side with their interests. The Egyptians wanted the Americans to not take a formal part in the negotiation besides mediation at best, and the British were shocked that the U.S. was willing to adopt the Egyptian position on how to structure the discussions over a possible withdrawal of British troops. In response, Churchill threatened to withdraw troops from Korea. In fact, he apparently said at the time that if the U.S. concluded an arms deal with Nasser, he would withdraw troops from Korea. Then he decided on a more diplomatic way to harm U.S. interests, by entirely ignoring the American position on the Soviets. Eisenhower gave a major speech taking a hard line on the Soviets, and despite Eisenhower's objections, Churchill proceeded to propose a trip to the Soviet Union on his own to the Soviets, and then in the middle of American-Egyptian arms negotiations (in fact, on the day that Dulles arrived in Cairo), gave a speech proposing an American-Soviet summit, related in Ike's Gamble by Mike Doran.
Obviously, the idea of arms sales to the Egyptians was concerning to the Israelis as well. This was coupled with the UN failures I mentioned above. The United States did little to enforce UN resolutions, same with other states, that had called on Egypt repeatedly to end restrictions on international commerce through the Suez. That was the case since at least September 1951, in UNSC Resolution 95, and was reaffirmed by UNSC Resolution 118 just a few weeks before the Suez Crisis. The failure to take any action to enforce these resolutions had arguably meant Israel felt both isolated and distrustful of an ineffective international system for maintaining order and international law, and was willing to take military action to alter that status quo. As Alfred Atherton argues in The Suez-Sinai Crisis (edited by Troen and Shemesh), the U.S. miscalculated by failing to take action on these UN resolutions, providing support for Nasser (though by the end of the Aswan Dam project in 1956, they had begun to see him for what he was, which was unfriendly to the West), and being willing to make arms deals with Egypt but unwilling to make deals with Israel.
Ultimately, the decision to side with Egypt was only by proxy a decision to side with the Soviets, and related to far more than the UN Charter, which the U.S. hadn't taken serious action to uphold when those actions were in Israel's favor, as with the UNSC resolutions mentioned above. To be quite honest, the UN has appeared in my view to be an afterthought and justification after the fact for the U.S. decision, rather than the actual reason the decision was made. It certainly wasn't something the U.S. viewed as a consistently important thing; after all, the U.S. expected (and received) British indifference to U.S. violations of the UN Charter with the toppling of the Guatemalan government by the CIA in 1954. It doesn't really need mentioning, but I'll do it anyways; just consider the Mossadegh toppling in Iran. Clearly, Eisenhower was amply willing to ignore UN principles when it favored U.S. interests. That's perhaps the biggest flaw in the top response on this thread, which doesn't really talk much about the Suez Crisis.
It wasn't even Nasser who convinced Eisenhower. Doran points out that throughout the crisis, Eisenhower was distinctly unfriendly to Egypt. In December 1956, he called Nasser an "evil influence", and said he shared the British and French opinion of him, but disagreed with their timing, and the "incident" they used to "launch corrective measures". The real reason he chose as he did, I'd argue, is because of his view of Arab-Israeli wars. He believed that the Tripartite Declaration to prevent aggression was a solid mechanism for stabilizing any Arab-Israeli war, even if the British and French were joining an aggression. The UN was a vehicle for his ire, but that doesn't explain why he chose how he did. It wasn't that he believed that the UN's principles were crucial. He viewed the UN as a tool to uphold his beliefs. The beliefs were what caused him to side against U.S. allies at the UN. In short, I'd argue the other answer gets it backwards. To give an analogy, the other user is claiming that if I hammer in a nail, I did so because I wanted to use the hammer. That's not true. The goal was to hammer in the nail, and the hammer was simply the best tool for that.
His beliefs extended beyond simply believing that the Tripartite Declaration laid out a good method for stabilization. He felt betrayed, of course, having told the British multiple times that he did not support any such action against Egypt. Even more importantly, and the reason for his statements to that effect, Eisenhower deeply felt that any war of this sort would drive the "Third World" directly towards the Soviets. He spoke publicly of the need for respecting international norms, saying they were "the soundest hope for peace in the world". But the President then convened a National Security Council meeting, where Foster Dulles pointed directly to the fear of losing the Third World to the Soviet orbit if they sided with Egypt. In fact, almost no time at all in that meeting is devoted to the question of preserving international norms for their own sakes; everything listed in the FRUS series of that meeting relates primarily to whether or not supporting an aggressor would result in bad geopolitical outcomes for the U.S., rather than discussing it in terms of moral outcomes. It's therefore entirely surprising to me that the other answer claims that the Cold War "had little influence" in the Crisis. For the U.S. decision, it most certainly did have a serious influence on decisionmaking.
So to sum up, the U.S.'s main reasons were:
A larger amount of friendliness before the Crisis meant the U.S. was less keen on war with Egypt, though they didn't like Nasser one bit by wartime.
The U.S. felt betrayed because it didn't believe a war was the best way to handle Nasser, and viewed it as detrimental to its interests in the region and even to Israeli security.
The U.S. believed any war would lead to a real weakening of its position among the Third World, and therefore sought to avoid damage to its relations there by taking the lead against its traditional allies to fend off criticism of joining their war.
Eisenhower in particular felt that the only way to prevent the Crisis from escalating into a larger Arab-Israeli war was to prevent any aggression as defined by existing American-British-French treaties, even if the British and French were not in agreement that this constituted a disallowed aggression.
Sources:
Mike Doran, Ike's Gamble
FRUS Series linked here
Cole Kingseed, Eisenhower and the Suez Crisis of 1956
S.I. Troen and Moshe Shemesh, The Suez-Sinai Crisis, 1956: Retrospective and Reappraisal, particularly the Alfred Atherton chapter titled "The United States and the Suez Crisis: The Uses and Limits of Diplomacy".