Your professor is right that the plague did deal the final blow to the kingdom of Lordaeron, but he is omitting the situation that the plague was introduced in. After the Second War, the alliance had begun to fracture with the Elves of Quel'Thalas leaving and the Kingdom of Alaric devestated by the retribution for their betrayal. Combine that with Thrall's rebellion and the bureaucratic incompotence in dealing with the crisis as well as the attention it and other Orc rebellions attracted (the Blackrock rebellion) led to a fertile ground for the Cult of the Damned to spread its plague.

Now interest in forbidden arcane arts had risen after the Draenor Expedition and the years of war with the orcs that had proceeded it which exposed the populous to orcish magics. Then, with many of the Horde's leadership, such as Grommash Hellscream and the Warcheif Ogrimmar Doomhammer, at large, the population questioned the sacrifices made in the precedeing wars. Former veterans, while many were happy to return home and raise a family, felt that they had given up many of the friends and a portion of their lives to defeat an enemy that was still lingering In the wilds while their children saw how they had sacrificed so much and received nothing in return began to lash out against the society that had abandoned them and experiement with dark magics.

Most in Lordaeron had only experienced necromancy because of the Horde's death knights. These dealings led to a increase in interest with Horde magics, and, with Antonides's studies of Orc magic still a ways away, humans began to try to replicate these arcane arts on their own. Without the guardians, no one was left to regulate these practices or the horrors that resulted from these twisted experiments.

This is the world the plague is introduced into. Kel'Thuzad found no problem recruiting members into these death cults that would go on to spread the plague. Context is important, but the plague results in the fall of Lordaeron. The Lich King's manipulation of Arthas led to the Culling and the massive expedition to Northrend which resulted in the loss of the entire ep edition but also a dwarves expedition led by Muridan Bronzebeard who was one of Arthas's victims (up yours, blizzard). Arthas would return, kill his father, and fracture his kingdom. The final blow to the Kingdom was the Burning Legion invasion, but the plague of undeath is the major cause of the fall. However the emphasis your professor puts on the role of Lich King (whose genius could fill a whole other post) is exaggerated.

You are correct to be skeptical, and it's a problem afflicting most interactive military history, and even the treatments that simulate 'eyes-on-the-ground' participation tend to reinforce a Great Man reading of events. The problem is compounded by the human-centrism of Alliance history; Horde historians have attempted to adapt the criticism as 'Great Orc,' then 'Great Tauren' and so on. 'Great Being' history doesn't have quite the same ring to it, though it at least escapes some part of the gender difficulty.

But I digress; the complications of achieving a cross-continental Azeroth Historical Association are dear to my heart as one of the founding dwarven signatories to the Association's charter.

Point is, understanding of Lordaeron's collapse as simply the Lich King's machination is not just a vast over-simplification, but also a political action on behalf of the monarchy. Monarchies manufacture ideologies, which isn't to say that Terenas Menethil II's reputation as a wise and just king is undeserved so much as it is to emphasize that there is another side to the story. (Personally, I find that Menethil's diplomatic skills are generally overrated by historians and his parenting was not nearly so bad as you might think, but that may be my propensity to contrariness.)

Do you think the infected grain spread itself? Disenfranchised, downtrodden peasantry took to a death cult for a reason, and that reason wasn't the dental plan. Monarchical interpretations don't allow for a dissatisfied populace choosing any option over the existing political structure, but that is in fact what happened.

The people took down Lordaeron, and if that isn't an indictment of monarchy I don't know what is.

Now, it's fair to say that they exchanged one monarch for another in a political struggle with a great amount of bloodshed and dying and undying. But robbing them of an active role in the events by attributing their actions to the Lich King is a historical disservice.

For more on the subject you might consider A Peasant's History of Azeroth by the famed (if somewhat controversial) undead historian Zinshadow.