Most do. It’s primarily the U.S. and Turkey that refuse to call it a genocide. Turkey denies it because they were the ones that did it. The Young Turks and subsequent regimes did a very thorough job of destroying records, the idea being that of no records existed to say otherwise, they could call it a “relocation” for the victims’ safety that just happened to go wrong in a few instances. The destruction wasn’t complete, thankfully, and several horrific documents still exist. Many are available at the Armenian genocide museum’s website. There’s one in particular, issued by Enver Pasha (The Ottoman Minister of War) if I remember correctly, that clarifies an earlier order, which says to not give regard to age or sex when killing Armenians. Basically, just kill them all. The Turks ended up blaming the deaths on unruly Kurds and convict battalions that supplemented the Ottoman army at the time.
To be clear, this is not an incident of “he said, she said”. They are numerous independent accounts of events during this period that corroborate the widely accepted narrative that the Young Turks simply wanted to finish what Sultans like Abdul Hanoi’s II had begun. The Ottomans has been killing Christians en masse for at least a century before the Armenian Genocide. Frederick Davis Greene deals with these in his late 19th century book The Sword of Mohamed. Some good contemporary accounts can be found in Dr Clarence Ussher’s An American Physician in Turkey, which deals mainly with the siege of the city of Van, and Henry Morgenthau’s Ambassador Morgenthau’s Story. Both were Americans in Turkey during the genocide. Peter Balakian’s Burning Tigris is a great book that details the period and explains what happened and why.
As for the American position, it’s entirely political. Turkey is a member of NATO, and the only member in the middle-east. The US has bases there, and it’s our primary staging ground for missions in the region. Due to this, the official position of the US government is to not call it a genocide. This isn’t new, but I’m not sure how far back it goes. Considering how erratic the current regime is, both in the US and in Turkey, it wouldn’t be surprising to see the US pull an about face on the issue.
At any rate, it’s a very under taught piece of history, especially considering that it directly influenced Hitler’s plans for the Holocaust. You see, the Germans had sent officers to the Ottoman Empire to help their new allies modernize their outdated military. Because of this, there were numerous Germans that observed the genocide occurring. At least one, whose name escapes me (Balakian discusses this in Burning Tigris) went back to Germany and later detailed what he saw to Hitler, who used those accounts to “improve” on the Ottoman methods. Instead of trapping victims in a cave and setting a fire to suffocate them, he created gas chambers. Instead of marching them to camps, he used trains because they were faster and less conspicuous. He even used the genocide to justify his own. When asked about the potential international response to killing millions of Jews, he simply said something along the lines of “nobody cared about the Armenians”.
Edit
Here’s some papers I wrote about it https://nersheti.wordpress.com/2017/07/17/the-great-calamity/
https://nersheti.wordpress.com/2017/07/17/the-battle-of-van/