Any discussion about war crimes in WWII should start with the atrocities committed by the axis powers. Between the holocaust, the German campaign in Russia, and the Japanese genocide in China at least 15 million civilians were killed, although some place the number closer to 30 or even 40 million if you include those who died from famines. In contrast, only around 1.5 million axis civilians died during the war. Source (sorry it's Wikipedia.)

War crimes were committed by both sides, but the numbers do not stack up in a way that makes them comparable.

There were rules of war as recognized by the warring parties. Some were more explicit like the Geneva and Hague conventions. Some were less so. But none of them really applied to bombings, because it was really a new form of warfare. Some bombings had taken place prior to WW2, but international norms had not yet developed. And although proposals had been made banning the use of aerial bombardments, no convention had yet been drafted or signed to that effect.

So during the war the recognized rules were more or less as follows: you could bomb military targets. You could bomb munitions plants and other manufacturing facilities as valid military targets. And because you couldn't really target anything with precision, basically cities were valid targets. And every side did this; the Axis, the Soviets, and the Western Allies.

So from a strictly "legal" point of view, it was legal, proper and appropriate. And everyone did it. The British and especially the Americans were just the only ones who built the massive strategic bombing fleets to do it on the Dresden-Hamburg-Tokyo type scale.

It should also be recognized that the "revisionist" historians do have some points.

First, the bombings were largely ineffectual, until the very last stages of of the war. Terror bombing or morale bombing never caused a people to petition their government to seek peace. And production bombing didn't do much to slow production. It was only in Germany when the US targeted petroleum and especially AVgas that it had a real impact on German military functions. And the city bombings and "de-housing" bombings only had production effects when they started killing hundreds of thousands of civilians, and leaving millions homeless.

And second, the bombings were a humanitarian nightmare. War is never fun for civilian populations. And the Western Allies in general did a pretty good job of trying to minimize civilian casualties. So the Air War stands in strange contrast to this general attitude. Deliberately burning women and children out of house and home is an atrocity. If it had been done by soldiers on the ground with flame throwers, the existing rules would have had them prosecuted. But because they were airmen dropping incendiaries from planes they weren't. None the less the intent was the same. And after the war the loophole was removed and air campaigns like they conducted, were made into war crimes. As Curtis LeMay put it "I suppose if I had lost the war, I would have been tried as a war criminal."

This isn't directly germane to your question, but for what it's worth, General Curtis LeMay, basically the author of Strategic Bombing in the Pacific was quoted as saying (years after):

"Killing Japanese didn't bother me very much at that time... I suppose if I had lost the war, I would have been tried as a war criminal.... Every soldier thinks something of the moral aspects of what he is doing. But all war is immoral and if you let that bother you, you're not a good soldier."

My point being that even those who perpetrated the 'Allied' crimes were cognizant of the moral murkiness of their actions. Thus, I think refute is probably the wrong aim - rather highlight the differences in scale & intention.

Source

A quick argument, aside from the difference in quantity, is that the bombings don't really compare with the intentional inhumanity of many of the Axis war crimes.

Civilian casualties as a result of military action against a military or war-industry target is deeply regrettable and the argument that the Allies did not do enough to minimize them has validity.

But when taken in comparison to the industrial nature of the death camps, using prisoners and civilians as slave labor to be worked to death, kidnapping women for use in rape camps, using human beings as test subjects for biological and chemical weapons and testing the limits of human survivability, I think the bombings come up short.

The bombings hurt civilians on a large scale, and it can be argued well that it qualified as a war crime. But it pales in comparison to the systematized dehumanization, exploitation, and extermination perpetrated by the Nazis and Japanese. War is never kind to civilians, but the bombings were never done with the blatant ideology that the victims were to be according the same level of dignity as livestock or animal pests.

I wouldn't understand why people would consider Allied bombing to be a war crime, when there are plenty of other actions by the Allies that could in fact be considered war crimes. Like mutilating dead soldiers and taking body parts as trophies. Or a general refusal to take prisoners (although admittedly this may partly have to do with Japanese soldiers pretending to surrender only to turn on their captors later). Or the rape of Berlin. Or bombing a historical monastery that the Germans had made perfectly clear was not garrisoned and had only the local abbot and some monks and two guards to deter looters.

But even all this pales to the sheer slaughter that members of the Axis inflicted on both surrendered combatants and non-combatants. Like Unit 731, the Japanese biological weapons testing unit that used live humans as test subjects. Or Japanese submarines machinegunning survivors and making them walk the plank (see: I-8). Or Einsatzgruppen. I'm not even talking about the Holocaust, the Rape of Nanking, the slaughter of many Allied POWs through either execution or hard labor or starvation, comfort women, rape, and so forth.

War is hell.