This question and similar have come up several times. There's always more to be said, but here are some notable threads that I think do a good job talking about the different ways Turkish public memory does or doesn't engage with the Armenian Genocide.

• /u/shaikann has a fantastic answer in Why does Turkey deny the Armenian genocide so vehemently when the genocide was done by the Ottomans, not the current Turkish state?, which gives three different types of denials (there were no killings; there were killings but it was a war time necessity; there were atrocities but the they were committed by the Kurds). I'll say I have encountered all three, even sometimes from the same person. I'd say there's also another layer, which I emphasize, that the whole period is characterized by the sociologist Rogers Brubaker calls "the unmixing of peoples". This rarely emphasized, but one of the main ways Europe ends up with fairly neat nation states.

There is also a level of genocide denial that argues that it can't be genocide because the killings and expulsion of Christians almost exclusively took place in Eastern Anatolia, leaving the Christian populations of Western Anatolia (including Istanbul) largely unmolested. This is true, but this is quibbling about what exactly "genocide" means, which I think is precisely the wrong way to approach the question of "what happened". That said, understanding this facet is crucial to understanding the genocide--this was in large part instigated by who would control the land, the territory of Eastern Anatolia, particularly after the crushing defeats of the First Balkans Wars. It's important to realize that the Balkan Wars put the birth places of a plurality of the ruling Young Turks outside the Ottoman Empire, and there was a real fear that the post-War outcome in Eastern Anatolia would similar unless drastic steps were taken. Some European sociologists and historians (Uğur Ümit Üngör most prominently) see the Armenian genocide as a larger Young Turk/Turkish Republican strategy of "social engineering".

Furthermore, some Turkish historians and citizens feel that Turkey is being unfairly blamed for what's a fairly normal practice--after all, the 19th century was characterized by massive "unmixing of peoples" (both flight by minorities and expulsion by majorities) where in Turkic and other Muslim populations had leave their homelands in the newly independent Balkan states and in the parts of the Caucasus newly conquered by Russia and ended up in the Ottoman Empire. There is a sense that this a double standard, and because Muslims were the perpetrators and Christians were the victims it some how has more value. I think this view obviously misses the scale and systematic nature of the Armenian genocide compared to earlier events in the Balkans and Caucasus, but it is certainly an important context for the Armenian genocide that is often omitted. It doesn't justify denying what happened to Armenians (and Greeks and Syrians--I actually don't like the term "the Armenian Genocide" in part because it doesn't recognize the larger policy aims of the CUP government), but there is important context to Armenian Genocide before the 1894 Hamidian massacres, which is frequently where short histories of the murder and expulsion of Anatolian Christians start.

Yet another layer is that the term "genocide" was coined in 1943, adopted as international law after World War II, and some people argue in Turkey that it ipso facto should be applied retroactively.

Getting back to other questions,

• u/Georgy_K_Zhukov and I have a back and forth in this thread Questions on the Armenian Genocide that I think is worth reading.

• I have another long post called The Armenian Genocide. Why is the current democratic Turkish Republic so defensive about something that was the responsibility of the despotic Ottoman Empire? which I think goes a little more into the overlapping relationship between the late Ottoman and Early Republican governments, and why the clean break on paper doesn't feel like as clean a break for many in Turkey. I have a line in there where I said "In Turkey, much of the debate is based on 'what they're saying about our grandfathers'" and I think that captures a lot of emotion of it--why it's not just a dry academic for many in Turkey (I think it goes without saying it is similarly not simply a dry academic discussion for most Armenians, either, especially the descendants of survivors). I feel like this is the single most comprehensive answer to this question on Reddit, so if you only read one, you can start here, but I also like it as a culmination of other smaller threads because I don't quite touch on everything but I try to tie a lot together into a historical narrative. Some of the follow ups go even deeper into related questions.