This is an age old question, and I think can be answered a number of ways depending on how you define the word democracy and fascism. In general I think throughout history you'll find that most states have some aspects of both fascism and democracy. They are not really mutually exclusive.

The word fascism is based on the Latin word Fasces, which is a tightly packed bundle of wood. In ancient times, people recognized that bundling otherwise weak pieces of wood together in a tightly wound stack created a structure that was much stronger than the individuals. And so fascism is a manifestation of this concept - the idea if that people bind themselves together as a nation toward the national interest, rather than individual interests, it makes the state stronger. But democracy can still exist within this construct.

The best historical example I can think of that depicts the tensions of "fascist" concepts and "democratic" concepts is in Classic Greek Antiquity and the conflicts between Athens and Sparta. A common view among modern people is that the Athenians were free democratic nation, and the Spartans were ruled by an undemocratic despotism. Indeed, Sparta did resemble a totalitarian fascist state in a lot of ways - men were forced to be soldiers, racism was prominent, and slavery was common and integral to the city-state's entire power structure. However, it is less known that Sparta was actually a democracy at its roots. Free citizens known has homoioi had the ability to vote on and influence laws. In fact, it could be argued that these free citizens were the driving force of Spartan politics over Sparta's kings.

The Athenian form of democracy was not so different, but clearly not as militarily focused, and probably more inclusive than Sparta's. It's hard to say how exactly the Spartans would have seen the Athenian system given that we have precious few direct sources on the internal politics of Sparta, but we do know from Thucydides that Sparta and it's allies were alarmed at the wanton aggression of the Athenian empire. A Spartan might say that the Athenian form of government leads to mob rule and aggression against its allies. They might believe that a militaristic "fascist" society leads to better enforced peace because soldiers better understand the concept of war. This is speculation, of course. I do think this topic does require a certain amount of it though, because the difference between fascism and democracy is not clear cut nor is it mutually exclusive.

I feel like the best answer to this can be found in Eric Hoffer's book about the rise of the Nazis (and other violent extremist movements), The True Believer, especially in light of Robert Altemeyer's book on the psychology of far-right authoritarianism, The Authoritarians.

The fascist argument goes like this: there was a time when People Like You ran the world. It was a lost golden age. Everybody was better off, even the people who aren't like you, because People Like You are just plain better at ruling the world. But there are a tiny minority, People Like Them, who were jealous of our power, and they conspired to overthrow People Like You and seize control of the levers of power. And that is why you didn't get the job you wanted, why your girlfriend or wife left you and took the kids: People Like Them stole it from you. But some day, People Like You will band together and take power back from the evil People Like Them, and everybody will be better off.

Then, to keep the People Like Them from stealing your job and your girl and your kids ever again, People Like You need to be so strong that nobody will ever mess with People Like You again, and pure enough from every form of impurity and filth that People Like You never lose their strength. People Like You need to dedicate your lives to strengthening the State, need to make sure that whenever there is something the State needs the banks will happily lend to it and need to make sure that the arms manufacturers and the army get everything they could possibly want in order to keep People Like You safe, and women and the church are instructed to raise Children Like You to be strong and pure.

One concept was the German one of "volk". It was. Sort of romanticized notion of authoritarianism, where people strove to build the greatest state by becoming one mass of people under autocratic control. G. Stanley Hall was.ropornet of it.

It's important to differentiate fascism from other right wing movements before looking at it's justifications; most people consider the Nazis fascist, and they definitely considered themselves fascists, but Nazism tends to borrow more heavily from Stalinism than the orthodox fascists, who you mostly find in Latin, Catholic countries. While less revolutionary (in the right wing sense) than Nazism, Fascism is itself more revolutionary than more conservative, less ideological right wing governments and movements. Landowners using the military to stifle calls for reform aren't die hard ideologues like the blackshirts, waving daggers in the air as they parade down the street, and old school conservative monarchists can face opposition from more radical right wingers when the king is believed to have liberal sympathies (like how Salazar declined to restore the king of Portugal).

That noted, it's best to think of fascism as an interwar phenomenon, occasioned by the collapse and loss of legitimacy by the society's traditional elites. Stressing the importance of hierarchy in society, the fascists aim less at a restoration of the old elites or conservation of the present order than at a reconstruction of hierarchy by imposing the structure of the party on the country as a whole.

Besides being an interwar phenomenon, orthodox fascism has been identified more often in traditionally catholic countries in Southern Europe, and the original fascists recognized this as well; northern Europe, and especially protestant Europe, was considered too individualist and too independent for proper fascism. They'd already overthrown what had been the dominant authority of the age, so spreading fascism, to say nothing of international fascism, didn't have much mileage among early fascists. As it happened, of course, Northern Europe did prove all too susceptible to radical mass movements, and you did see a fascist alliance between Germany and Italy, but the first doesn't concern theory, and the second was borne of opportunism (both countries had lots to gain at the expense of the old Franco-British world order).

So, programs and arguments. The fascists base their worldview and arguments on the near universality and necessity of hierarchical relationships in society; to them, by breaking people up into atomic individuals, you ignore the relationships that give meaning to their lives and give them a distinct identity. One of the key programs of the fascists is the corporate state. Instead of seeking to represent individuals, the fascists seek to represent groups that share common identities. In formulating policy, they seek to sate the interests of the various groups represented, and to make sure they're all working towards the interests of the state; capitalists, specific industries, labor (remember, Mussolini got his start as a syndicalist), the Church, and so on would be considered as discrete entities, not as coincidental conglomerations of individuals. They want a fundamental harmony between everyone who supports their state and society, and woe be to those who stand in their way.

To fascists, individualist, liberal democracy doesn't acknowledge the fundamentals of human nature: that we live as members of relationships, and that we relate to each other from positions of superiority or inferiority. Pure Democracy doesn't take nationhood, occupation, religion, age, sex, wealth, or the interests of the state into account, but these are all fundamental to modern societies, and even those of us who believe in equality before the law still recognize and understand their importance.

This is of course highly theoretical; turns out populist, radical movements can become absurdly corrupt, and the various internal and external pressures, as well as the idiosyncrasities of Mussolini and Hitler, doomed and damned the concept forever, but I think it's a mistake to think of fascism as pure self serving demagoguery (even though it certainly was that).