It is pretty easy to annoy an academic these days, especially those who study international relations. And this does the trick
Preventive war and pre-emptive war are two entirely different things. While I got schooled on twitter that these are not legal terms, they basically are in terms of how the world perceives them.
Pre-emptive war: launching a first strike when the other side is about to attack. Imminence is key AND first strike advantages are hugely important. If there is no advantage in attacking first, one can wait out a first strike. When pre-emptive war is in the air, it makes war more likely because both sides fear that the other side will strike first. World War I is the cardinal example for IR types even if the reality of that war's start are more complex. The best example of this in recent times is the Arab-Israel War of 1967. While that war produced a heap of confusion afterwards, Israel striking as the Arab states were about to launch a war is not seen as illegimate, and, given how near a thing the 1973 war was, not a dumb thing to do. Pearl Harbor was not pre-emptive since the US was not about to launch a first strike against Japan, although it could be considered preventive.
Preventive war: striking now before the balance of power shifts against oneself. Far less legitimate since war is not inevitable, and there are many ways to deal with relative decline of oneself and rise of one's potential adversary. Attacking Iraq in 2003 was a preventive war, as it was an effort to prevent Iraq from getting weapons of mass destruction. Sure, they didn't find any, but that was the asserted justification. Germany's motivations prior to WWI were in part the desire to deal with Russia before it became too powerful.
Pre-emptive war can be legitimate--that self-defense may include stopping an attack before it happens with an attack of one's own. Denying the rise of an adversary by launching a war is not seen as legitimate. The US lost a heap of legitimacy in 2003 by starting a war that it did not have to fight.
The funny thing is that talk of pre-emptive war with regards to North Korea is rather, um, silly. Why? Because any first strike by the US will almost certainly fail to destroy North Korea's ability to wreak havoc and rain destruction upon Seoul, Tokyo and other populated areas in the neighborhood. But this is not really so funny since the North Koreans might be concerned enough about losing their ability to retaliate that they react hastily to signs that the US might be preparing a first strike. That is, talk of preemptive war may make war more likely. Which makes McMaster's talk very bad policy.
As I have argued before, this notion that we are running out of time and that military options are the only ones available are likely to cause a devastating war that can be avoided. It may be that North Korea wants more than just maintaining its regime, but it is certain that they care most about that and this talk of pre-emption does not encourage patience or other stabilizing behavior.
So perhaps the McMaster quote is a misquote, but I think it is part of a larger dynamic in DC: that the Trump administration, including McMaster, does not seem to understand the basics of international relations. That NATO is not a protection racket nor a country club. That protecting one's economy from international competition will lead to retaliation and on and on. Alas, Trump does not study nor read, so I don't expect him to learn no matter how basic IR 101 is.