We present a novel way of learning skills of object interactions on entity-centric environments, whose goal is to learn primitive behaviors that can control objects and induce their interactions without external reward or supervision being used. Existing skill discovery methods are limited to locomotion, simple navigation tasks, or single-object manipulation tasks, mostly not inducing useful behaviors of inducing interaction between objects. Unlike a monolithic representation usually used in prior skill learning methods, we propose to use a structured goal representation that can query and scope which objects to interact with, which can serve a basis for solving more complex downstream tasks. We design a novel counter- factual intrinsic reward from either forward model or successor features that can learn an interaction skill between a pair of objects given as a goal. Through experiments on continuous control environments such as Magnetic Block and 2.5-D Stacking Box, we demonstrate that an agent can learn object interaction behaviors (e.g., attaching or stacking one block to another) without any external rewards or domain-specific knowledge.