The occasion is the murder of her beloved General Zhukov, taken out on Gaad's order in retaliation for the murder of Stan's partner Chris a few weeks ago. Up until now, Elizabeth has shown herself more likely than husband Phillip to use the "wet" solution, i.e., shoot an opponent or a target dead. She starts out determined to do this to whoever ordered Zhukov's assassination. When we find out that the guy she gets strapped into a chair with her gun to his head is not Gaad, and was only following orders, we expect Elizabeth to kill him anyway, since he was at least in part responsible. And then she walks away from the imminent kill.
Why? She later explains to Claudia that she figured out that Claudia was playing her to kill whoever ordered Zhukov's killing - because Claudia loved him, too - and Elizabeth doesn't like being manipulated. But that doesn't ring completely true. If Elizabeth had already felt, on her own, that she wanted retribution for what happened to Zhukov, she would have pulled the trigger whether she felt she was being manipulated or not.
So her reason, I think, is her continuing Americanization, or the growth of that part of her that feels like a normal American housewife in the 1980s, whatever exactly that is. And that's the great strength of the series - the tension between who Elizabeth and Phillip are and were, and who they are and are coming to be. As the killing escalates on both sides, this growth out of their origins as sleeper agents who just follow orders becomes even more riveting. Elizabeth and Phillip were strangely fascinating and dangerous to begin with. But they are becoming even more so with every episode and every piece of the story it delivers.
See also The Americans: True and Deep ... The Americans 1.4: Preventing World War III