You're equating a state - an entirely political entity - with a nation, which is a common misconception. Nations are a political consciousness based around a common culture, language, and people. In its simplest form, a Nation is the political side of an ethnic group, though it often is much more complicated than that. The term gets easily confused today because most states today centered around the Nation-State idea - that a State primarily consists of a single constituent Nation.

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However, this is a fairly recent phenomenon. The 19th Century would see a rise in nationalism that is often attributed to (or at least claimed to have been started around the time of) the French Revolution. Political consciousness among the masses became increasingly common, leading to calls for unification areas like Germany and Italy and independence in places like Ireland and much of the Habsburg monarchy. Prior to this nationalism, States didn't necessarily care about the social identities of the peoples they governed, and the legitimacy of a State, its policies, and its borders was reliant on other factors that varied with location and era. In the early and high middle ages, for example, the concept of Christendom and Papal authority was considered a chief source of legitimacy among Christian peoples, far outshining any local identities. Personal relationships between ruling elites providing legitimacy and power were another staple of Medieval Europe, especially in the early Carolingian Empire. Later on, as local identities began to form, special privileges took hold in many areas (though not necessarily as a result of the unique identity), but these separate identities themselves were rarely the cause of attempts for self-governance.

Take the Holy Roman Empire after the Reformation. Religious identity - Lutherans, Calvinists, and Catholics - became far more important than local identity, even in areas like Bohemia or the Netherlands where these identities were more developed. Rather, religion-based legitimacy continued to dominate, and, as the outbreak of the Bohemian Revolt in 1618 shows, the personal identity and relationships of rulers continued to hold more weight than the identity of the masses.

Really, up until the rise of nationalism, even states largely contained in regions we today associate with Nation-States (Britain, France, Spain) weren't so much defined by their people as their ruling dynasties and their domains. Diverse cultures and identities existed in all of these kingdoms - Britain had English, Welsh, Scottish, Irish, and a number of smaller cultural groups, France had Aquitanians, Waloons, and Bretons, and Spain had Galicians, Catalans, and Basques (to name a few). A major feature of the French Revolution was a sudden attempt to homogenize culture in hopes of creating a more "French" identity.

The 1848 Revolutions would mark a significant earlier wave of this nationalism, but we can see the trend of nationalism extend on through the 20th Century, often as a justification for wars and secessionist conflicts. Postcolonial states often offer examples of Nations clashing with States as new borders end up combining multiple nations that often are at odds with eachother. Many African civil wars can be traced to national conflicts - the Nigerian Civil War was largely an attempt by the Igbo Nation to secede from Nigeria, the secession of Katanga in 1960 attempted to justify its secession in part by drawing on the local ethnic group, and the civil wars in Angola and Ethiopia both saw belligerents on all sides heavily defined by national groups - often moreso than "pure" political ideology.

First a small premise, what is usually meant with "nations didn't exist before X" is that modern nations, or nation-states, did not exist. There is a fairly big difference between states, nations and nations-states.

As many terms is the realm of social sciences it's extremely hard to define what a nation-state as we all have a vague idea of what a nation is but when we try to write down a definition it often turns out to be too inclusive (so things that we would not call a nation are like calling the East India Company a nation because it had some of the attributes we would normally attribute to nations) or too exclusive (so things we think as nations aren't).

That being said it's generally accepted that for a state (that is a form of political organization that controls a land) to be a nation-state, it has to:

• Have some defined borders and accept the existance of other equal nations over which it has no control.
• Be sovereign with laws of it own that apply on its territory and the full capacity of modifing and altering those laws; this does not exclude volutary limitation of law making power such as partecipation in international organizations or treaties.
• A nation is thought by the members as the collective property of all the members, this does not mean that it has to be democratic.
• Finally, and probably most important, a nation is a group of people that think themselves as one and share some ethnic, historical, ideological, cultural and linguistical charateristic (for instance Japan shares all of them, the Us share mostly the latter four, indonesia mostly the ideology and the languange and so on...); so a nation-state is a state inhabited by a nation.

So why would many states of the past not be classified as nation-states; let's go step by step following the defitions given. The first one rules out many empires of the past like the chinese empire or the holy roman empire because they though themselves as universal, that is as having control over all of humankind often due to some moral/religious imperative to bring peace or prosperity in the world; so for instance the Holy Roman Emperor claimed to have the right given by God to rule over all christians; the Chinese emperor thought that he was the middle kingdom was by his superior customs, history and tradition the most advanced country in the world and belived that all nations were naturally subjects of the heavenly emperor. This rules also exludes nomadic nations that moved more or less frequently.

The second rule is particulary important in the context of europe; most european states were not sovereign but formally subjects of the empire or other states. Also the rulers had little power over laws, for the most part internal private law was governed by customs that varied by place to place; moreover in high courts, like the imperial chamber, roman law, as codified in the Corpus Iuris Civilis by Justinian, was used because prestigious and widely studied, not because it was the official law (custom law was more important, but you had to prove it's existance which was no easy task in most cases). This changed after the 30 years war when a new international system, the westphalian paradigm, started to appeart, that is the idea that states were sovereign and had the power to make law, sign treaties and that other states should not interfere with them and that the Holy Roman Emperor did not had universal power.

The continuos existance of semi autonomous organizations inside the state, with privileges and immunities, like the nobility and the church, over which the king had little power also violates this definition as the state does not have full sovereignity over the people; this is different from having legal rights like under a constitution or having different rights based on who you are because in those cases the state is autonomosly setting a law for which for instance it can force you to be catholic or women can't vote; while many privileges of the french kingdom were due to ancient rules that were more powerful than the King himself.

The third is regards the idea, commonly accepted in many states of the past especially in the east, that the state is the private property of the ruler. Republics were based on this idea (Res pubblica means the common wealth) but for monarchies the idea was that the country was made of what the king owned and the thing his vassals (be nobles, clergymen or cities) and everything on the king domain was his own. There was no difference between the king treasury and the state treasury and so on; this changed when Hobbes claimed that power comes from the people that delegated it to a king thorugh a social contract. Today most nations accepts (although often don't enforce) the idea that the nation not private property of the ruler.

Finally the last one is the reason most states were not nations is that the people did not felt a community; the idea of nations and that each nation should have his own country arised in the XIX century and probably if you asked someone from Brest in the XVI century who he was he would have probably said that he was a breton; states were held toghether by the king claimed divine right, by conquest or by family right, not by a common feeling of nationhood. Often they did not have any common language, controlled people with different ethnic and religious identity and shared no common history. Some nations controlled the state, but it often included other, legally inferior peoples.

So let's analyze the nations you cited:

• The English & French Monarchies are two exceptional cases because they checked many of the reuirements, although not perfectly. In general we can describe them as proto-nation states because there is the idea that they are a independent sovereign state and they share a culture or a history, but still it was not defined. The French state became a modern nation state, united by the language, after the revolutions when fedualism was eliminated, a constitution was encated and modern private law was born; for the english monarchy is harder to say because of the question of scotland.
• The roman empire was not culturally unified, and most people living in provinces did not think of themselves as roman, so it's difficult to call it a nation state; the same applies to the ottoman empire.

Your teacher is basically correct in the sense that the modern concept of the nation-state, and particularly the civilization-state, is a relatively new one (albeit its foundations are a little older than the 19th century). In our era, most of the world shares a generally common understanding of what a nation-state is and why they exist. In our understanding, cultures and civilizations often (although by no means always) line up roughly with national borders: Chinese people and Chinese culture exist primarily in China, Polish people and Polish culture exist primarily in Poland, etc. This culture/border alignment is a type of nation-state that has been termed a "civilization-state", contrasted with a nation-state like Belgium in whose borders exist multiple cultural groups speaking multiple languages yet still grounded, to one extent or another, in a meta-identity of sorts as Belgians. The United States follows a similar model. Ultimately, though, most of us on planet earth identify ourselves through the political identity of a nation-state, and most of us have a fairly coherent definition of what that nation-state is and what it represents.

But this paradigm, in which nation-states are the primary level of international political representation and virtually everyone on earth lives in one, is a fairly new one. If you rewind the clock back a few centuries you would find that there were relatively few nation-states in the modern sense. Germany and Italy, for example, existed as a patchwork of kingdoms and did not become unified nations until the second half of the 19th century. China & Japan had gone centuries on end of nominal unity but with little centralized authority where regional warlords held most political power. Many modern day nation-states, like Ireland or Mexico, existed as colonies during that time. Some of the biggest power players on the map in centuries past, such as Austria-Hungary, the Holy Roman Empire, or the Polish-Lithuanian Commonwealth, weren't nation states so much as confederations of different ethnic and cultural groups that had been politically fused together under a single government (generally a monarchy). These states generally fell apart eventually due to lack of a cohesive cultural identity around which a political identity could be built.

Modern nationalism, which can be said to have reached its zenith during WW2 but persists in to this day, really began to take shape during the 19th century. There were nation-states before the 19th century, like France and Russia, but it was not until this time that a modern understanding of what a "country" is, the relation of a government to its people, and how a national populace ought to view themselves, began to coalesce around a similar framework. These concepts solidified, not coincidentally, concurrently with the formation of Germany & Italy into united nations rather than various fiefdoms, not to mention decades of tumultuous French experimentation with what form a French nation-state truly ought to take.

Also around this time, the US Civil War was the first time that Americans first began speaking of their country as "the United States is", rather than "these United States are". That was rarely heard prior to the Civil War, but became the rule afterward. Speaking of the US Civil War, it sometimes confuses modern students that a man like Robert E. Lee would have felt more loyalty to his home state of Virginia than to his country of the United States. It is confusing to our sensibilities because 21st century people by and large don't think like that- not in the developed world, anyway. But regionalism (identifying with what region you're from rather than what country) was widespread throughout the world in that era and still persists in some places today. Just as many Americans in that era defined themselves firstly as "Virginians" or "Pennsylvanians", the French peasants who stormed the Bastille in 1789 did not see themselves as "French" so much as "Parisians", "Lorraineans", etc.

So, your teacher's claim is basically correct. Consider this: "I live in the nation of Stankonia. I am a Stankonian, and my parents were Stankonians. I vote in Stankonian elections and Stankonian is my first language. I am willing, if necessary, to serve in the Stankonian Army to defend Stankonia's borders". That is a distinctly modern way (or perhaps a distinctly 20th century way) of defining oneself and is still prevalent today, albeit less so than a century ago. But all of this, however, is a relatively recent development when viewed in the scope of human history. Recorded history goes back about 6,000 years, but the perspective I just described above is only about 200-250 years old.