Hi!

All citations at the bottom.

Few basic things that I can refer to that might help explain the relationships at play here. I'll refer to the relationships on the basis of different authors and how they view it.

Julian Amery, a British MP who holds Eden in high regard, claims in a book by Israeli historians Moshe Shemesh and Selwyn Ilan Troen that Eden underestimated the ambitions of Nasser. He argues that Eden wanted to withdraw from the Suez to achieve an understanding with Nasser from 1951 on, and he discusses in great length his own experiences during that time and how Eden had his own shortcomings:

The argument raged from 1951 onward. Sir Anthony Eden, then Foreign Secretary, judged that we should withdraw from the Suez Canal Zone altogether, if necessary. He did his best to keep something but he was prepared to go altogether. He believed this to be the condition of achieving an understanding with Nasser and, more important in his eyes, of securing American support for the defence of the Middle East. He was to be proved wrong on both counts. He underestimated altogether the extent of Nasser’s ambitions to lead the whole Arab world and to base his leadership on a crusade against British, and indeed, French imperialism. More seriously, he underestimated altogether the determination of the United States, good allies of Britain as they had been in the World War, to eliminate the influence of the European imperial powers from the Middle East and North Africa, as they had already begun to do in South-East Asia with the Dutch in Indonesia. Even he was persuaded by Washington that if Britain withdrew from the Canal Zone, the Americans would defend British interests in the Middle East, including the security of the Canal.

Pg. 87 of the book.

He goes on to point out that he blames Eden for what came after they withdrew, saying:

His decision to withdraw was a catastrophic gamble. Had we stayed Nasser could never have nationalized the Canal and could never have attacked Israel again. It can be quite difficult to stay put, but a damned sight more difficult to get back. Events were to prove Eden’s decision disastrous.

Pg. 88.

Robert Rhodes James, a British historian writing in the same book, claims that Eden was led astray but did not want to withdraw or get involved. He claims that it was a combination of multiple factors that led to the final decision, but argues that Eden had a deep respect for international law and agreements, and that Eden did not trust Nasser to uphold his with regards to the crucial Suez Canal. Coupling this with the emotional element associated with nationalization of a canal that "Tens of thousands of young men from Britain, Australia and New Zealand had fought for...in two world wars..." (Shemesh and Troen, 81), and he argues that it was Nasser who misjudged. James quotes Martin Wight on the issue, who said:

Eden’s moral dilemma has a lasting significance. In trying to preserve the political conditions of international life, he allowed himself to become unscrupulous... He explored the region of the moral universe of politics, with high-mindedness and self-righteousness, blindness and clear- sightedness, misjudgement and courage.

Pg. 83.

But it wasn't just a miscalculation on withdrawing in the first place, followed by a miscalculation of American support and Nasser's ambitions. He also (perhaps it isn't his fault but perhaps it is) unwittingly followed the advice of his own military advisers, according to James:

he was let down by his military advisers, who did not believe that the Israelis could possibly get to the Canal as quickly as they said they could. As it would take the Anglo-French armada six days to reach Port Said from Malta, it was time and not the Egyptians that destroyed him. For in those six days, and particularly after the R.A.F.’s bombing of Egyptian airfields, the storm broke nationally and internationally. With victory assured, the American pressure broke Macmillan and the Eden cabinet. All was then dismal aftermath.

Pg. 83.

Perhaps had he included the opposition parties, as James suggests on Pg. 82, he could have had more backup and withstood the pressure. Perhaps had he checked with more advisers, or gotten better advice in general, or believed the Israelis, the results might have been different, and international pressure wouldn't have been quick enough to stop the toppling of Nasser, which would have been viewed as a fait accompli. But these are speculations. The main criticisms leveled at him were misjudgments of Nasser's ambition first (in arguing to leave the Canal), then misjudgments of American support, and then getting bad advice (again, hard to say what he could've done better realistically given the strain he was under) from his military advisers. And as an undergrad history minor, I'm sure you know that hindsight is also 20/20, so it's easy to criticize but hard to imagine if anyone could have done a better job since we can't really test that theory.

Now I'll move on to another work, this one by G. C. Peden, British historian, which argues that:

Eden’s miscalculation of American reactions to the attack on Egypt was damaging to Britain’s reputation and fatal for his career, but there had been no illusions in Whitehall about Britain’s ability to act contrary to American wishes.

Pg. 1095.

This is the most frequently leveled criticism of Eden's miscalculations and the resulting crisis, as far as I've seen. Also:

In the event, Eden’s agreement with Nasser in 1954 for the withdrawal of all British forces from Egypt did not dissuade the Egyptian dictator from spreading anti-British propaganda, opposing the extension of the Baghdad Pact, or importing arms from the Soviet bloc. By the spring of 1956, the Americans had given up on Nasser as a possible partner in solving Arab–Israeli disputes, and were willing to co-operate with the British in curbing his power by economic and other indirect means. However, as in 1951, this support did not extend to countenancing the use of force that would alienate Middle Eastern opinion.

Pg. 1082-83.

Two more quick notes by other authors. Kingseed, an American army veteran and historian, claims that Eisenhower miscalculated when he didn't see Eden's next move coming, saying Eisenhower overestimated Eden's commitment to "the alliance":

Eisenhower chose to believe that Eden would never adopt a military campaign in Egypt without prior consultation with the United States. So convinced was he of Eden's loyalty to the Anglo-American partnership, that Eisenhower underestimated the prime minister's capacity and willingness to act in the crisis in contravention to the expressed desires of the president of the United States. It was a serious miscalculation on Eisenhower's part and led to an even greater crisis in the Atlantic alliance.

Pg. 80.

This reinforces the idea that Eden miscalculated the American support for British policy, and how they would react. Eisenhower is quoted on pg. 81 of that book as saying:

Bombs, by god. What does Anthony think he's doing? Why is he doing this to me?

So there's yet more from an American perspective that this was all not expected and all not liked by the Americans.

And from another perspective, that of Kunz (another American historian), she also notes that Eden was one of the foremost people calling for a strategic withdrawal from the Suez. Against the opposition of the right-wing "Suez Group", he prevailed and got withdrawal to happen. She also notes that the British miscalculated the American position, and relied on support: same as other historians.

Those appear the be the miscalculations presented by historians throughout the four sources I've got on me to look through. To sum up, they are:

• Miscalculating the likelihood that the United States would side with Britain in the Suez Crisis.

• Miscalculating the benefits and future (along with Nasser's ambition) of the Suez if Britain withdrew (as it did) earlier in the 1950s.

• Miscalculating the efficacy of Israeli forces and how quickly they would advance, by not believing them.

If you have more specific questions, please let me know and I'll elaborate!

Kingseed, Cole C. Eisenhower and the Suez Crisis of 1956. Baton Rouge: Louisiana State UP, 1995. Print.

Kunz, Diane B. The Economic Diplomacy of the Suez Crisis. Chapel Hill: U of North Carolina, 1991. Print.

Peden, G. C. "Suez And Britain's Decline As A World Power." The Historical Journal 55.04 (2012): 1073-096. Web.

Troen, S. Ilan, and Moshe Shemesh. The Suez-Sinai Crisis, 1956: Retrospective and Reappraisal. New York: Columbia UP, 1990. Print.