I don’t see that there’s any other answer than ‘it depends’. More particularly, it depends on why your teacher has decided to frame the Second World War in this way.
I’m coming at this from a perspective of someone who studies (and teaches) a conflict whose relationship to the Second World War is quite debatable. A classic exam-style question for college students who study modern European history is ‘Was the Spanish Civil War the opening phase of the Second World War?’. It’s asked not because there is a right or wrong answer, but because it depends entirely on how you define the crucial issues at stake, and you can make a valid argument either way. For instance, if the Second World War is defined as an anti-fascist war, then it makes sense to view Spain as the beginning of this wider conflict; the opening blows in a wider ideological war. But if the Second World War is about something else – not least because the war in Asia and the Pacific doesn’t map neatly into a fascist/anti-fascist divide – then it no longer makes sense to view Spain as part of the same conflict. Your exam answer depends entirely on the frame of reference you want to adopt.
In this case, I can think of several reasons why someone might want to frame the conflict in the ways that your teacher wanted to. For instance, in terms of simple arithmetic, these are the theatres that saw the highest numbers of deaths. For both Germany and Japan, I believe there’s a case to be made that these were considered the most important fronts to achieve their aims, and generally saw the largest allocation of resources, though I’d gladly defer to an expert on either war effort on the extent this held true over time. Equally, there are reasons why it’s spurious – the influence of the United States, especially in terms of industrial production, was far too large to entirely discount in this way. The territory and populations that were won and lost in the ‘comparatively small’ conflicts were massive by any reasonable standard, and those that suffered occupation, displacement, exploitation and extermination could justifiably challenge any version of the conflict that so blithely downplayed their experiences.
But more importantly, I think, there’s a pedagogical case to be made for radically reframing the conflict for students. I don’t think any conflict has been the subject of national myth-making to the extent that the Second World War has, from the Battle of Britain, to Omaha Beach, to the French Resistance and more. There is a tendency to emphasise certain national perspectives, which in turn often leads to distorted impressions of how the war was won or lost. Challenging students’ understanding of what was important about the Second World War, going beyond the frame of reference that is provided in popular culture and high school history, is a useful way of showing students that things can look very different from perspectives other than the ones we grew up with. In other words, showing that studying history is not just about memorising dates and events, but being critical and flexible in how we approach the past.
Tl;dr: if your professor has presented this view as divine truth, then there are many reasons to question it. But if, as seems more likely, they are challenging you to rethink the way you’ve framed the Second World War up until now, then they're just doing their job.
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