In order to give some appropriate context, I will explain why my teacher said this by rewording his reasoning from memory.
With the Edict of Caracalla, Roman citizenship is extended to include everybody under emperor rule. While this is good for increasing the income of the empire by having more citizens to tax, it destroyed the legitimacy of original citizens and of Rome, the city, itself. Rome may have adopted cultural aspects from those it conquered, but there was still a distinct dominant Roman culture that was higher than all others. Only citizens were fit to serve in the army and the Italian peninsula is the major source of Roman culture and citizens. It is the capital region of the empire and shadows all others.
Once Caracalla enacts his edict, suddenly Roman citizenship is no longer a privilege or even something special. Everybody is equal, from the relatively recently "civilized" Dacians to the true-blooded Romans of noble houses. The Italian peninsula loses its legitimacy as the dominant region of the empire because now every corner of the empire provides citizens, soldiers, etc. With everybody on an equal playing surface, peoples of different regions have just as much legitimacy to have power and wealth as the next group. So why should Rome, and the emperor, Princeps/First-Citizen have all the glory? To serve the Empire used to mean giving your life to Rome. Now it can include, Gaul, Iberia, Anatolia. This edict decentralized the authority of Rome, its emperor, the original citizens, and their culture. The effects of this can be seen in the crisis of the 3rd century where the empire fractures regionally and privatized armies emerge again (the comitatus of Gallienus). Even after reunification, the empire is never really the same again and the writing is on the walls for the end of Roman hegemony.
My teacher is big on the terms hegemony and legitimacy. In his definition, hegemony is the forceful ability to rule over others through conquest. Legitimacy is the ability to maintain that authority through being accepted as the rightful leader by those being ruled.
Of course, he attributed other reasons for why the empire fell, but he was assured that the Edict of Caracalla was as major as any other factor contributing to the end of Rome.
I've heard many reasons/explanations as to why the west "fell," but this is the first time I've heard this one. I'm going to assume by "broke the Roman Empire," he/you means began the decline of the west. There are a few major issues with this:
The first being that after the crisis of the 3rd century ended, the Roman empire was reunified and relatively stable, even in the west for over one hundred years.
The second is that he seems to be locked into a paradigm of "Roman superiority" that doesn't really exist. The Roman army had been recruiting from colonies for over a century before Caracalla. While these are technically "Roman citizens," these are people from current day Spain, France, and even the Balkans. Roman identity is a very tricky thing. Are you a "true Roman" if you are a Roman citizen pre-Caracalla, but still have never been to the city of Rome, or maybe even Italy? I would argue that you are.
I would be more willing to accept that the west never fully recovered from the crisis of the 3rd century as an argument, but he'd have to connect the edict of Caracalla to that, first. Even then, it isn't that cut and dry. I would also entertain that 4th century Rome, even in the west, is the most prosperous the western empire ever was, outside of the Antonine Age.
So, no, I don't agree that the effects were as "severe" (regarding the eventual "decline and fall" of the western Roman empire) as your teacher is suggesting. In some ways, I think it made it stronger.
Certainly it was a major blow to the empire, but it was not the only, or even the most significant factor in the Western Empire's collapse. The Empire fell into it's crisis period after Caracalla, yes, but it stabilized under Diocletian and Constantine, and the Eastern Empire lasted until 1452 with the edict in full effect. As a general rule, if someone tries to tell you that "The Roman Empire fell because of X", with no context, they are either uninformed, or are trying to sell an ideology. The Roman Empire fell for an immeasurable number of reasons. To simplify those into a single reason is a simplification to the point of deception.
To answer your implied question of "What were some other factors that contributed more to the Roman Empire's fall than the Edict of Caracalla", I would argue that several were more significant, such as:
Note that none of these claim sole responsibility for the fall of the Empire, but together, they lead to the Western Empire's eventual decline and fall.
I've certainly heard that argument before, and his logic is not so wrong as to completely toss his idea out.
The main problem is, this is one of a long long long long list of potential causes people like to blame for the fall of the empire.
Everyone with a modern agenda tends to use the Fall of Rome and their interpretation to the "why" of the fall as their precedent to make their modern political cases. Take Ron Paul and his blaming of the fall of Rome on inflation, or anti-immigrant nationalists in Europe who blame barbarian migration.
However with this said, your teacher's emphasis on "true-blooded" Romans shows an alarming unfamiliarity with current research which shows a far more complex fluidity to even late Roman identity than simply "blood."
In a nutshell, your teacher tends to overgeneralize his understanding of the empire, its army recruitment and the impact of the edict. However there are nuggets of truth there that I can see other scholars arguing from (and some probably already have).
As I stated in some recent threads, I personally like JB Bury's explanation for the fall of western empire. Which is simply: bad luck.
Why? Because bad luck can happen to any empire, whereas the search for that ONE cause of its decline, makes it seem as if its fall was inevitable, which skews history toward oversimplification.
Empires and history are complex things. If we really had a grand unified theory that could explain everything, we'd be able to predict the future as well. But often, it's not that we've found a simple model that predicts how events in history should've unfolded, but that we've contorted a model to fit the complex shape of history.
Which is really no model at all.
While citizenship became more widespread, it also became 'less valuable'. It didn't offer the protections it once did. When the relative amount of non-citizens decreased, a new distinction emerged: people were now divided in honestiores and humiliores.
"Certain kinds of punishment, such as corporal punishment by being thrown to the wild beasts or by being crucified, were the lot of the convicted humilioris. The lowest class of free citizens of the Empire, subject to such examination and punishment as had once been applicable only to slaves and to free citizens in cases of treason, had now slipped juridcally down to that level itself. Citizenship no longer offered the protection to all citizens it once had done."
From Torture, by Edward Peter, page 27. Available on Google Books.
"While in the early Principate period, Roman penal law distinguished primarily between citizens and non-citizens and this was the criterion in terms of personal rights for the determination of punitive measures, from the end of the 2nd cent. AD social rank determined the treatment of individuals by the courts. The differentiation in punishments is linked in the legal texts and in modern research primarily with two terms, honestiores and humiliores. The honestiores were the members of the privileged classes (senators, equites, decurions, veterans); they were exempted from to…"
http://referenceworks.brillonline.com/entries/brill-s-new-pauly/honestiores-humiliores-e517020
Doubtful.
It is always tricky to convincingly demonstrate that something done two hundred years ago is really the specific cause of something happening now.
I mean, if somebody claimed that a specific law passed in 1812 is the only or principal reason of today economic crisis (for example), that would require a huge burden of proof from him, don't you think ?
It is not exactly that those two centuries were uneventful, and that the fortunes of the Roman Empire did not swing a lot.
By the way, before the date of the edict of Caracalla (2012) there had been emperors born in Africa, France and Spain.