One approach to argue against that general thesis, is to point to the changes that have occurred in historical examples. If they’re arguing about the limitations of the EU and Brexit, you might compare what Europe was like before the EU, and how much has changed in the direction of “globalization”, and what relations between Europe and the rest of the world were like before and after the EU… but of course one would need solid definitions of terms first.
The term “globalization” seems to be easier to find definitions for than “cultural regionalism”, but the definitions even for that term differ from each other significantly:
* “the development of an increasingly integrated global economy marked especially by free trade, free flow of capital, and the tapping of cheaper foreign labor markets”
* “Globalization means the speedup of movements and exchanges (of human beings, goods, and services, capital, technologies or cultural practices) all over the planet.
* “the process by which businesses or other organizations develop international influence or start operating on an international scale.”
* “Globalization is [...] the growing interdependence of the world’s economies, cultures, and populations, brought about by cross-border trade in goods and services, technology, and flows of investment, people, and information.”
I would start with studying this Stanford Encyclopedia of Philosophy article: https://plato.stanford.edu/entries/globalization/
Which says in part:
“In contemporary popular discourse, globalization often functions as little more than a synonym for one or more of the following phenomena: the pursuit of classical liberal (or “free market”) policies in the world economy (“economic liberalization”), the growing dominance of western (or even American) forms of political, economic, and cultural life (“westernization” or “Americanization”), a global political order built on liberal notions of international law (the “global liberal order”), the proliferation of new information technologies (the “Internet Revolution”), as well as the notion that humanity stands at the threshold of realizing one single unified community in which major sources of social conflict have vanished (“global integration”). Globalization is a politically-contested phenomenon about which there are significant disagreements and struggles, with a growing number of nationalist and populist movements and leaders worldwide (including Turkey’s Recep Erdoğan, Poland’s Jaroslaw Kacyzńki, Hungary’s Viktor Orbán, and US President Donald Trump) pushing back against what they view as its unappealing features. Fortunately, recent social theory has formulated a more precise concept of globalization than those typically offered by politicians and pundits. Although sharp differences continue to separate participants in the ongoing debate about the term, most contemporary social theorists endorse the view that globalization refers to fundamental changes in the spatial and temporal contours of social existence, according to which the significance of space or territory undergoes shifts in the face of a no less dramatic acceleration in the temporal structure of crucial forms of human activity.”
As for “cultural regionalism”, I would challenge the debate instructor to offer even one appropriate and complete definition for that phrase. Say that (as I have) you have looked at over a dozen academic articles and books that mention the term, often in their title, but they all fail to define what they are talking about.
So starting with the basic and most authoritative sources, the Oxford English Dictionary defines “regionalism” as:
“The theory or practice of regional rather than central systems of administration or economic, cultural, or political affiliation.”
or
“A linguistic feature peculiar to a particular region and not part of the standard language of a country.” https://www.lexico.com/definition/regionalism
Which is a very sane place to start, and has almost NOTHING to do with whatever political science term the debate question seems to be alluding to.
Ask the instructor at least for pointers to where one might find a definition of that term!