In a diff-in-diff or regression discontinuity research design, why is it important to describe why the counterfactual is a plausible one? I've heard it mentioned that in difference-in-differences, regression discontinuity, or even in some other quasi-experimental research designs, that the counterfactual should be explained as a plausible outcome. I'm feeling dumb and can't wrap my head around why that's important though. Is it to explain that without the research, the counterfactual would have happened and its implications? Isn't it basic intuition that treatment relates just to the treatment group? Any explanation would be much appreciated.

In a quasi-experimental design, the comparison group is constructed to look as close as possible to the treatment group just prior to the intervention. All covariates are balanced in about the same proportion as the treatment design. And if you randomly selected 1 person from the treatment and comparison group, it would be difficult to determine who was a member of the treated group and who was not, based upon the before treatment variables.
The only discernable difference is that the comparison group did not go thru the treatment program. Some members of the comparision group may also have had the same outcome as the treatment group, and some may not.  But the critical point is that is you can show statistically that enough of the comparison group had the same positive outcome as the treatment group, that would be consider the counterfactual, and there would not be enough evidence for treatment success.
