What you're experiencing is the difference between how scientists tell their own history and how actual historians would tell it. It is an interesting phenomena (one that has been studied by historians, anthropologists, and sociologists of science) but you should not confuse it with the serious study of history of science.

Scientists deploy history in a very selective and non-rigorous way, but it serves a professional function. Historians (following Thomas Kuhn) have called this "textbook history of science," i.e., the kind of history of science you'd get from a science textbook. This approach is generally a variety of Great Man history that we might call Great Genius history, in which the history of science is a progression of individuals who came up with important and usually correct ideas that either built upon or overthrew some previous idea.

This is not how historians of science tend to talk about it. We talk about collections of people, institutions, cultural/political/national contexts, and often spend as much time reconstructing the importance of the wrong/overthrown idea, as well as pointing out the many ways in which the idea that overthrew it was often not totally justified or correct either. Through this approach, we have found, one gets a much more complete understanding of the messy way in which science has worked over time, and one sees better the interaction not only between the context and the people, but the context and the content of science as well. This approach tends to make scientists unhappy because they prefer an epistemic model in which the content of science is independent of context — they see science as developing "universal truths," not truths that are somewhat contingent on, say, European politics in the interwar period.

The "textbook history" that they teach is not meant to be a full education in history; it is meant to be a mnemonic for understanding the conceptual development of the modern version of the field (and thus excludes anything or anyone who doesn't in some way contribute to that), and it is meant to model a sort of virtuous idea of what a scientist is meant to be (pioneering geniuses coming up with new discoveries or ideas). Whether that is a good social function or not can be debated (given the collaborative and team-based nature of most scientific work today, the over-emphasis on individuals is potentially very misleading, and it has been demonstrated empirically that fields that think "genius" is the main factor behind success tend to be extremely exclusionary to other forms of contributions and also, for whatever reason, tend to be worse about things like misogyny and racism, transplanting broader social archetypes about the types of people who are "geniuses" into the social expectations of the work), but that seems to be what the goal of it is. It is certainly a different goal from the historians of science, in any case.

There are good reasons to talk about contexts (which Zeitgeist could be a code for), and many historians of science have long done so, although they would expand that term probably broader than the scientists tend to. Kuhn's work on paradigms for example are a version of this, but one that applies to the larger context of ideas as well (e.g. it is not just about what kind of place or time you live, but the dominant worldviews that exist, and in Kuhn's model a truly new scientific "revolution" is a revolution of worldviews more than it is specifics of a theory or discoveries).

Much of the study of modern science is the study of essentially Western science, for reasons both justifiable and not. Justifiable in that Western science became linked to Western hegemony more generally in the 19th and 20th centuries, and thus in many places is something more like a Global Science than a specifically Western endeavor at this point; unjustifiable in that it is often about ignorance of what was going on in other locations and the ways in which those things did influence the development of Western/Global Science as well (this is especially the case if one is looking further back in time, when the Middle East and Asia were more dominant in the sciences). Historians of science do look far broader geographically, even in the modern period, and also spend a lot of time looking at how knowledge flows within and between different cultures and contexts.

But it is important to remember that the version of the history of your field they are giving you is a very narrow one, meant to talk about how history built up along a path to get to the big questions they think are important today. Occasionally in the service of doing this they'll explore a now-discredited idea (often as a contrast to how we do things today), but they are still showing you history through a narrow perspective. In psychology that will typically mean focusing on the German, Austrian, and American story, especially if you are an American (there is a "well-worn" version of the history of psychology that is highly influenced by Freud, for example). This is not your individual instructor's fault, most likely — this is because this is the way they were taught it, and it is the rare scientist who actually does any serious study of the history of science.

If you are interested in reading something that will delve more into the context, Ellenberger's The Discovery of the Unconscious is a very richly done close examination of 19th century Vienna and its impact on Freud, Breuer, and the others in those early circles. Thomas Kuhn's The Structure of Scientific Revolutions has nothing much in it on the history of psychology but is considered a good introduction to thinking about the differences between the kind of science history that scientists tell and the kind that historians tell, though Kuhn is not at all the last word on the latter. If you want to read a very different sort of history of psychology, check out Lemov's World as Laboratory — it's quite a contrast to what you are likely being taught!

In addition to /u/restricteddata's very good points, I'm someone who specifically teaches a history of psychology class. I'm not entirely sure what level of psychology you're being taught, or the context of why you're being taught about psychology's histories, but there's also a likelihood that you might come across English people seen as big influential names in psychology (Charles Darwin and Francis Galton, the people who put together the statistics used in psychology like Ronald Fisher, etc), Swiss (Jung, Piaget), and Russian (Pavlov, Vygotsky, maybe Luria) - your instructors might not have gotten to them yet!

There's a bunch of different pedagogical reasons for teaching psychology students about history, some of which don't have much to do with the accuracy of that history. For example, I can imagine that your instructors might be trying to impress upon students the extent to which their thinking is a product of a set of ways of being educated about the world in the 21st century in a Western country. There's a movement within psychology at the moment to discuss the typical psychology experiment that research is based on as being 'WEIRD', where WEIRD is an acronym standing for Western, Educated, Industrialised, Rich, and Democratic; as a result the assumptions of psychology also depend on the society in which that research is done, and your instructors may well be trying to get you to think about and understand those assumptions. There's also something of a tendency of whiggish or Great Man thinking in history in science classes (including psychology) - it's easier to just talk about Freud in a class than to explain about him in context (I half suspect that this is why your instructors talk about the Zeitgeist, because they're trying to place Freud in context - modern American society is different in some important ways to the one Freud lived in, and Freud's theories - as imperfect as they were - were meant to reflect that society).

Additionally, the typical history of psychology is very much a history of American psychology and its intellectual influences. One reason why the 'fathers' are often German, Austrian or American is because American and German psychology traditions are the oldest explicitly experimental traditions (though psychology and psychological theorising was long a part of philosophy before this, and should not be discounted). In the American tradition, Anglophone psychology is understandably prominent, and German-speaking psychological traditions are quite prominent, not least because German-speaking psychologists often ended up in American psychology departments in the early 20th century, and then even more with the exodus of Jewish peoples from Germanic lands; these people all contributed to making American psychology the way it was. This is not necessarily reflective of psychology in the rest of the world - psychodynamic theories apparently held on for much longer in Spanish- or Portuguese-speaking countries, for example - but the American psychology tradition is reflected elsewhere because America has a tendency to be influential given its prominence in 20th century and 21st century life in general.