I've always understood that the Israeli attack in the Six-Day War was very much a justified pre-emptive attack. It appears that this may not be supported by evidence and that there was no actual threat to Israel in 1967. What do we know about the reasons for war?

Now that you've answered my question about what spawned your question, I'll do my best to respond.

First thing's first; not many argue credibly that there was no threat to Israel. There were hundreds of thousands of troops mobilized on its borders, Arab leaders were giving speeches about destroying Israel, it was blockaded in the Straits of Tiran by Egypt, and Egyptian planes had overflown Israel's nuclear facility at Dimona. The Arab armies were joined together by a joint defensive pact. There is no way to argue credibly that there was no threat to Israel. That said, the extent of the threat is disputed. Note that this does not matter for the perspective of the laws of war. So long as Israel had a reasonable expectation with the information it sought, and sought to de-escalate and launched war only as a "last resort", most theorists and lawyers would argue it was easily within its right to self-defense, and is perhaps the best "self-defense" case of pre-emption that exists (no perfect such test exists). Consider the words of preeminent just war theorist Michael Walzer in Just and Unjust Wars, where he says:

Israeli anxiety during those weeks seems an almost classical example of "just fear" - first, because Israel really was in danger (as foreign observers readily agreed), and second, because it was Nasser's intention to put it in danger. He said this often enough, but it is also and more importantly true that his military moves served no other, more limited goal.

The Israeli first strike is, I think, a clear case of legitimate an anticipation.

That aside, however, the historical perspective is muddled by the lack of Arab records as well as the often-distorted perspectives that cloud judgment on the issue.

Quigley discusses Operation Dawn himself, but so does Oren. Both have their own biases. Oren has always been an historian, but he has also had pro-Israel biases. Quigley has always been a law professor, but he has also had anti-Israel biases.

Quigley primarily disputes Operation Dawn's importance in The Six-Day War and Israeli Self-Defense. There, he argues that the historical evidence for Dawn is "thin", that Nasser did not know about it, and says that the United States did not take the threat seriously. This is completely at odds with Oren's telling, who says that the United States took it seriously enough to transmit a thinly veiled threat to the USSR (and thereby to Nasser), and that Nasser said he did not want war to the USSR when confronted on the subject but knew that Operation Dawn was in the works.

It's hard to investigate either side's claims. I don't have access to the Arab texts, and Quigley's sources are not available on the source I have access to either at the moment. Maybe I can revisit that later. In the meantime, other authors also have conflicting views. Segev casts doubt on the veracity of the Israeli claims, saying they were meant to pressure the United States, but the Israeli intelligence assessment, he concedes, did say the Egyptians were showing signs of preparing "not only a holding action but also an assault". Israeli historical documents, based on seized Egyptian documents, are quite clear in asserting that the Egyptians did in fact order the attack, to start on May 27, but that they called it off. That is where the most current Israeli research sits, and the dispute is unlikely to be resolved anytime soon. To pretend that there is "little evidence" this was not close to launch or a threat to Israel is false. While Israel may have indeed exaggerated the threat to attempt to get U.S. support, that does not mean the opposite (there was no threat) is automatically true.

Next I will move to The Nation's article here that you mentioned.

This article is riddled with problems. Not only does it make use of the widely-seen-as-bigoted term "Jewish Lobby" in describing why Donald Neff's book's claim about why Washington "allowed Israel to launch the Six Day War", it contains misrepresentations of the books it purports to summarize.

There is no clear "trend" in opinion on the 1967 war that turns against it. The real "trend" has primarily been one of dispute, which has only been marginally alleviated by document releases over the years. Most in the West and Israel still regard Israel as in the right, while others continue to deny this. Unfortunately, the politics involved can often interfere with the history.

The problematic portrayal begins with a discussion of Donald Neff. No discussion thereby is complete without noting that Neff began to lose his credibility over the years by distorting documents and history to attack Israel, including writing works funded by wealthy Palestinian families on behalf of Palestinian think-tanks. Neff made numerous claims in his later years that the goal of all pro-Israel presidents has been to win the "Jewish vote", and that they sacrificed U.S. interests to do so, something that is incredibly problematic and false. Similarly, it is problematic to pretend that the United States "allowed" Israel to attack Egypt, as though it was fine with as much and only allowed it because of "pressure". This is wholly inaccurate and has no real backing.

The author of the article proceeds to slam Oren by doing two things: 1) Noting his biases; and 2) Discussing Oren's opinions on the Iraq War. Ignoring that 2) is irrelevant entirely, the author also pretends that Oren's comparison between Saddam and Nasser shows he implicitly supported the Iraq War. But the article does not truly do this, and is instead focused on new research about the 1967 war, and only references Saddam as an example to hook reader interest; Oren was a prominent opponent of the Iraq War.

The author then dives into Segev's work in earnest. Here he misrepresents the work. You'll notice, of course, that none of his article has really discussed any level of Arab responsibility to this point. Segev is discussed in the same vein. He claims that Segev says Rabin drew a dovish cabinet into conflict. But Rabin, who suffered a nervous breakdown in the weeks leading up to the war at the thought of conflict, was not proposing to "escalate" conflict with Syria "with impunity". In fact, Rabin's proposal was to re-establish deterrence in response to Syrian tank fire. Segev does not actually make the claim, anywhere I can see, that the generals were responsible for the war, or pushed heavily for it. It's true that a general nicknamed "Gandhi" proposed war, and Rabin supported him doing so, while Eshkol did not support this. But this discussion was held back in February, months before the war, and was proposed as a resolution to the ongoing terrorism and skirmishes with Syria to re-establish deterrence. This was not a proposal that led to the Six Day War. Nor did the generals lead to the Egyptian decision to "deter" Israel from attacking Syria. Indeed, it is rather strange that anyone could discuss this without noting, as Segev does, that Egypt's troops being sent to the Sinai were in response to a false Soviet intelligence report. Segev argues that this was not necessary to spark the crisis, given Israeli remarks prior to the war, but it's rather indisputable that it did spark the crisis as the immediate cause, and that Israeli statements were not solely some push by the "generals".

What is perhaps most curious about the article, besides its glaring omissions and its misrepresentations of the works it discusses, is that it essentially ignores other seminal works on the 1967 war. It paints a trend on the basis of primarily three works, and does so rather poorly. Nor does it actually prove that there was little to no threat of external attack. Even Gluska, who notes the army "pressuring" the government, and which the author references, writes in The Israeli Military and the Origins of the 1967 War that the pressure came following the Egyptian blockade, well into the crisis. Israel does not change from victim to aggressor in this narrative, but rather remains victim; the army's pressure was because they, as Gluska writes, thought that "war was now inevitable" thanks to the blockade. Israel's army therefore pushed for preemptive war because of the threat, as Gluska writes, saying that the army grew "concerned at the growing activity between the Arab states and at the frenetic mood of the Arab world", and saying also that delays might "bind Israel's hands and give the Egyptian army respite to consolidate its positions in Sinai or perhaps even to initiate offensive action". Furthermore, Gluska writes convincingly of the Israeli perspective from a larger perspective that is often missing from Segev and the article's claims:

Even if no Arab action was taken, the presence of an offensive and threatening military concentration, however static, along Israel’s borders, would force Israel to maintain mobilized reserves in the long term, thereby paralysing the economy. In order to interrupt this dangerous development in good time, the army considered it essential to take the initiative as soon as possible, and above all to ensure dominance in the air.

The army was therefore not seeking aggression or to seize territory, but to prevent the state's economy from collapsing and prevent vulnerability. Israel definitely had this fear, and there is good reason to think it had the right to be afraid, as I mentioned above, if only because of the economic point of view, let alone the debate about Operation Dawn.