Search Result Explanation (SeRE) aims to improve search sessions' effectiveness and efficiency by helping users interpret documents' relevance. Existing works mostly focus on factual explanation, i.e. to find/generate supporting evidence about documents' relevance to search queries. However, research in cognitive sciences has shown that human explanations are contrastive i.e. people explain an observed event using some counterfactual events; such explanations reduce cognitive load and provide actionable insights. Though already proven effective in machine learning and NLP communities, there lacks a strict formulation on how counterfactual explanations should be defined and structured, in the context of web search. In this paper, we first discuss the possible formulation of counterfactual explanations in the IR context. Next, we formulate a suite of desiderata for counterfactual explanation in SeRE task and corresponding automatic metrics. With this desiderata, we propose a method named \textbf{C}ounter\textbf{F}actual \textbf{E}diting for Search Research \textbf{E}xplanation (\textbf{CFE2}). CFE2 provides pairwise counterfactual explanations for document pairs within a search engine result page. Our experiments on five public search datasets demonstrate that CFE2 can significantly outperform baselines in both automatic metrics and human evaluations.