This piece gives a Cliff Notes version of neoconservatism that I found helpful as it connected some dots I hadn't recognized before. It's worth a read, beginning with a bulleted list of its essential elements, but here's a few other highlights, bold added:

Neoconservatism is much more of a worldview than a coherent political ideology. That worldview has been shaped by rather traumatic historic events, most notably the Nazi Holocaust and the events of the 1930s that led up to it. Of course, the Great Depression and pervasive anti-Semitism were important causes. But neoconservatives also stress three others: the failure of liberal institutions in the Weimar Republic to prevent the rise of Nazism in Germany, the appeasement of Hitler by the western European democracies and their failure to confront him militarily early on, and the “isolationism” practiced by the United States during this fateful period.

This assessment leads neoconservatives to believe that spineless liberals, military weakness, diplomatic appeasement, and American isolationism are ever-present threats that must be fought against at all costs. This is an integral part of their worldview, and you can often hear it in their polemics. For them, the importance of maintaining overwhelming military power—or what they call “peace through strength”—as well as constant American engagement, or unilateral intervention, if necessary, outside its borders cannot be overstated.

The latter point is particularly critical because neocons believe that, in the absence of a tangible threat to our national security, Americans naturally retreat into isolationism. As a result, they have engaged in a consistent pattern of threat-inflation—or fear-mongering—over the past 40 years, from Team B’s exaggeration of alleged Soviet preparations for nuclear war in the mid-1970s to the hyping of the various threats allegedly posed by Iraq, radical Islamists, and Iran after 9/11.

In their Manichean world, neocons see the U.S. as the ultimate white hat.

...like the U.S. itself, Israel is also seen as morally exceptional due in major part to the fact that its birth as an independent state was made possible by the terrible legacy of the Holocaust and the guilt it provoked, particularly in the West. Moreover, its depiction in the media since 1967 as both a staunch U.S. ally and a lonely outpost of democracy and Western civilization besieged by hostile, if not barbaric, neighbors has contributed to this notion of moral superiority. Of course, its most recent wars, its treatment of Palestinians, and the steadily rightward drift of its governments have made this image increasingly hard to sustain, not only in the West, but within the Jewish community here as well.

[Neocons] believe that both the U.S. and Israel are morally exceptional. That means that neither one should necessarily be bound by international norms or institutions, like the UN Security Council, that would constrain their ability to defend themselves or pre-empt threats as they see fit.