The argument concerns what motive persons are acting under when they kill. No one on 'Team Theist' has made even the slightest attempt to engage, let alone deny, the fact that a great deal of killing in human history has been done with explicitly religious motives, even to the point of being required as a matter of doctrine taught to believers. The only response has been to claim that atheists have killed a great many people, a plain fact which no one on 'Team Atheist' would think of denying, but in making this response, there has not been, and will not ever be, a successful attempt to demonstrate this is in any way required by atheism, in the same sense that a great deal of killing can be traced directly to actual doctrines and dogmas and ritual practices of various religions.
Communism, and for that matter Anarchism in its late nineteenth and early twentieth century form, viewed religion, specifically locally dominant Christian sects, as a major prop of the Capitalist order, as one of the forces arrayed to keep working people quiescent in the face of the injustice routinely perpetrated against them by an exploitative social order. By and large (there were exceptions) these Christian bodies regarded Communists, Socialists, Anarchists, Syndicalists, indeed just about anybody agitating and organizing and acting to end the exploitative economic order in the here and now, as damnable criminals at war with the order God ordained. In short, each regarded itself as at war with the other, and behaved accordingly. Where this war became more concrete reality than metaphoric hyperbole, people were killed, and they were killed in the struggle over what the economic, social and political order of a place was going to be. Where Communists came to power, first in Russia, they did indeed attack religion, just as they attacked aristocracy and property. The Orthodox Church took an active role in the counter-revolution embodied in the Civil War, and clergy looked on the killing of Reds just as enthusiastically as commissars watched their firing squads at work. As matters developed, the clergy came out on the losing end of that fight, and there are consequences for this. The Communist government set out quite conciously to break anything that had taken part in or lent support to or even offered potential grounds for counter-revolution, considering this a necessity for consolidating the revolution and establishing the new Communist order.
Matters in China followed a somewhat different path, and certainly featured a great deal less singling out of religion, as religion occupies a somewhat different space in Chinese society than it does in the West. There was some specific antagonism towards missionaries and Christianity, but this had more to do with long-standing xenophobia and resentments of the privileged position Christians came to enjoy in the latter days of the Ch'ing Dynasty, and whole system of foreign privilege bound up in the 'Unequal Treaties'.