The earliest example I find of this is the American Civil War with Sherman's famous quote "War is Hell." However in antiquity and seemingly up until around the 19th century war was much more romanticized and glorified. What happened, was it simply a result of things like photography coming around?
The Crimean War is a good example of a turning point in this regard, as it was the first "reported" war in the sense that we know today. Nowadays we have reporters in Syria (for example) who have access to the battle zones and the surrounding areas, and the Crimean War is largely considered to be the first war in which this happened.
It's a heavily criticised war in the UK partially because of this. With the likes of William Russell (reporter for The Times) and Roger Fenton (photographer) people saw war for the first time, and because of the technological limitations of photography back then, all that could really be captured were still scenes before and after battle. Regarding Russell, the public could now read independent reports of the war without military censorship, and so they began to learn how war really was like between the "glorious victories" they'd come to expect from war.
Fast forward to the First World War and you have people seeing these horrors firsthand, in Belgium and France due to the destruction of their homes and the like, and in Britain with German raids. Add to this the sheer numbers of men who fought (and so a lot to spread the reality of the front line through correspondence, when on leave etc.) and the casualty lists which ordinary people had access to, and war is now one of the worst experiences anyone can face.
Remember that before these times, all people at home heard was when the victory was achieved and how it was done (usually as told by the military leader who won the battle), so in order to increase their standing (the Duke of Wellington is a good example here) leaders would speak very positively about their experiences. In other cases, people like Lord Tennyson (poet laureate during the Crimea) were government-appointed and so would write positive works because of this.
So overall a lot of this revulsion is due to the increasing presence of the media over time. Looking at the Vietnam War, it's highly controversial because of the amount of photography which was allowed, which brought the conflict into people's homes for all to see.
There really isn't a definitive start date. Different cultures see war differently at different times. Jewish texts have an overwhelmingly negative view of war after the failed revolts against the Romans, presumably because they'd seen the negative aspects of entering wars that proved fruitless.
What leads you to the conclusion that war was more "romanticized and glorified" in the past? While I won't deny that attitude existed in the past, it certainly wasn't universal. My suspicion is that war was glorified in texts you've seen because you've read things written by the winners, who are much more likely to have a less-rosy view of war.
You can actually see both sides of the argument in Homer's Illiad, one of the oldest texts we have. There are people in it who see war as glorious, as one of the best ways to obtain that most-wanted commodity "undying fame." But the war itself, and the people who fought in it on both sides, are unflinchingly portrayed as awful, as lawless and brutal, even by the standards of the day.
This is a really interesting question! I suspect the "red herring" answer to this question is the Kellogg–Briand Pact, or more officially the "General Treaty for Renunciation of War as an Instrument of National Policy". This was a 1928 agreement to make war an illegitimate tool of foreign policy, and is one of the reasons why countries today gavotte through hoops to make the other side legally the "aggressor" in a conflict.
But I said that was a red herring, right? I'd like to add my military science point of view to /u/gingerkid1234's statement, because I believe it to be correct. Different cultures place different understandings on different periods of war - not necessarily linear from "glorious" to "slaughter". I would like to nuance it though, in a couple of ways.
I would like to talk about the military science idea of "cultural mobilisation" or "the first of Clausewitz's Triangles"
I would like to talk about the concept of "ambivalence" within that mobilisation
Cultural mobilisation is the reorientation of society from peace-time rhetoric and activity into a state which will support warfare and resist an enemy. Think of the British in World War One; before the war the leaders 'primed the pump' as it were by making speeches warning of the danger to revered institutions, the mass-media printed stories supporting belligerence, and grassroots conversations created a situation in which a war could be fought - not would be fought, but if something did happen then the entire society would support the war. And in the First World War, Britain did; not the massive outpouring of popular excitement that pop history would remember, but a steadfast support regardless.
This "support of the war" is actually critical. The German thinker Carl von Clausewitz reckoned that a war can only be sustained if three elements of society support one another mutually; the military, the government, and the people. If any one of these three loses the willingness to continue to fight then the triangle fractures and the war will end.
Okay, part one down. Part two is "ambivalence". This is exactly what it says on the tin; that people can have multiple, competing, contradictory understandings of something, and ideas about war are absolutely just a tangled mess when it comes to meaning. As /u/InfamousBrad points out, elements of "war is hell" come into play very early on in descriptions of western war, along with "war is manly" and "war is glorious". All of these elements are present, and even though they seem contradictory, human beings are wonderful things, and will totally accept that ambivalence. When people discuss a particular war with one another, some of these ideas are more important than others, which creates a certain tone for a particular war's remembrance. The Second World War is remembered as a 'good' war, the Vietnam war is remembered as an 'unnecessary' war, etc. This ambivalence means a war is both glorious and wasteful, full of manly courage and endurance while also being bloody and futile.
Vietnam, by the way, is often spoken of as when "television changed the way we understood war" which is a load of bollocks. Television made splitting the Clausewitz triangle more efficient; suddenly you didn't have to kill so many Americans to prey on the ambivalence western people hold about war, and thus pry the people away from either the military or the government.
I have no idea how to make a TL:DR for this; I'm afraid you're going to have to read it. I am also in the awkward place of being unsure about where general knowledge about war stuff ends. If I don't make sense, please ask questions!