Oh my gosh! This is my thing! I have some things already written on it that I sent to a friend recently, and I'll do my best to amend them to reflect your teacher's points and your question.

Your teacher was probably referring to a notion sometimes held by modern historians and art historians that creating a metaphorical representation of tragedy is difficult because any metaphor associated with a tragedy is ruined by association with it, and does not do any actual good as a piece of art in remembrance of the loss. In my experience, this view has been best expressed by Jay Winter, the editor of the most recent edition of the Cambridge Histories of the First World War. Winter has written several books about memorialization of the Great War, including "Sites of Memory, Sites of Mourning" and "Remembering War," in which this idea appears. He usually applies the idea your professor was talking about specifically in terms of the Holocaust, discussing the difficulty of creating an effective Holocaust museum without lessening the tragedy or misrepresenting loss. However, the idea that it's difficult to make a meaningful memorial to such a large loss is quite applicable to many other things as well. I've studied the application of the idea specifically to Great War memorials, so that's what I'm going to talk about in answer to your main question about how memorials are designed.

One of the reasons that memorials sometimes fail is that experiences with huge wars are extremely personal: no two neighborhoods, divisions, or even soldiers will have experiences that can be captured meaningfully by the same piece of artwork. (See Winter's "Sites of Memory" for more on the individualization of loss in the Great War.) As such, the most effective memorials are often those created by people who have been effected by the conflict which they are memorializing. In the Great War, Britain's Foreign Office operated a propaganda unit called Wellington House, and several notable artists of the period were dispatched by it to the Western Front to create sketches and drawing of the War (see most any cultural history of the War for more info on this highly interesting project; I like Robb's "British Culture and the First World War"). Some of these artists had already been veterans themselves, discharged for minor injuries. Other veterans actually created artwork while still at the Front, or at least began to create it; there's an artist named Eric Kennington who claimed to have created an oil-on-glass portrait while carrying the work from location to location on the Front (this has been pretty heavily disputed, and I haven't found evidence of it in his archives, but he definitely did make it within a month or two of his discharge at the latest). When the War was over, these veteran artists were often either hired by the government or took up private commissions to create memorials, and their artwork is some of the most striking post-war memorial work done after the Great War. (See ERIC KENNINGTON 1917-1918 on microfilm in the War Artist's Archive, Imperial War Museum London, Scates and Wheatley on War Memorials in the Cambridge Histories, Winter's Sites of Memory and the FANTASTIC "The Great War in Modern Memory" by Paul Fussell for more about either Kennington, the war artists, or the memorials they made).

Differences in the memorials made by affected artists and those less affected by the War are many and varied, but I'll try to give a rundown of a few major ones here. Please note that these characteristics are not by any means limited to memorials created by veteran-artists -- I'm just arguing that they are more likely to be seen in memorials created by those who fought or were personally affected by fighting.

• Pre-Great War memorials rarely showed individual infantrymen, preferring to focus on the glory of generals and other commanders. Post-War memorials were more likely to depict individual soldiers, the rank and file of the War.
• Some church memorials attempted to avoid showing visions of damaged human bodies or war images in favor of a more sanitized memorial listing names and commending souls to God. Veteran-artist memorials almost always show actual human figures, often armed, if not actually wounded.
• The absence of almost all writing on memorials was a trend that emerged around this time and became quite popular as a memorial response to the Holocaust; Winter argued that removing imagery from a memorial and leaving a huge, blank chunk of stone was a way to physically represent a "hole" in society that was impossible to close. I would argue that memorials with lots of writing do this less effectively than huge memorials with very little text.

I hope this has helped! If you want to look them up, some of my favorite memorial sites are London's Cenotaph, the Machine Gun Corps Memorial at Hyde Park Corner, and the 58th London Division Memorial at Chipilly, France. All of those sites have characteristics of veteran memorials such as those I described above.

In short, I suppose the answer to the question "how were memorials designed" by my understanding is that these veteran-artists did their best to recreate their experiences in artwork! I believe that answer applies to the Second World War as well.

Edit: Lest my words be misinterpreted, I want to emphasize that what is considered a "good" memorial will change drastically from person to person, and historian to historian. The factors I described about how better Great War sites were designed by artists are by no means exhaustive or definitive. They are just my opinions based on my reading and research :)