We typically explain phenomena by citing their causes. Yet, we also explain phenomena without citing their causes, for instance by referring instead to mathematical theorems. To account for the explanatory power of such non-causal explanations, several philosophers aim to free the interventionist theory of causal explanation from its causal component: interventions. The resulting counterfactual theory of causal and non-causal explanation claims that X explains Y iff Y counterfactually depends on changes in X. While initially attractive, such a counterfactual theory faces a familiar problem: explanations are typically asymmetric while not all counterfactual dependence is. The challenge of asymmetry demands to qualify a counterfactual theory such as to account for the asymmetry of explanations. First, I reject two potential solutions to this challenge: amendments of a counterfactual theory using Lewisian semantics or two inference schemes that tell us when to infer that X explains Y and not vice versa. Second, I develop a quasi-interventionist version of a counterfactual theory apt to deal with explanatory asymmetry, in two steps. I identify a class of explanations that a counterfactual theory without further specification already claims to be asymmetric. And I develop the notion of a quasi-intervention to account for the asymmetry of most remaining explanations. The resulting quasi-interventionist theory claims that X explains Y iff Y counterfactually depends on changes in X brought about by a quasi-intervention. Finally, I suggest accepting the symmetry this quasi-interventionist theory entails for a particular class of non-causal explanations.