Recent work in Human-Robot Interaction (HRI) investigates the role of human users as teachers from which robots can flexibly learn new personalised skills through interaction. However, existing human-robot teaching methods remain largely unintuitive for the end user and require significant effort to adapt to the way the robot learns. This paper envisions the use of dog training methods as a starting point for HRI researchers to develop more intuitive interactions between human teachers and robot learners. We provide a design framework (called FETCH-R) aimed at guiding the conception of interactions between human teachers and robot learners inspired by dog training. This work paves the way towards the use of animal training as an inspiration to create human-robot teaching protocols that promote engagement, ease-of-use, and fosters human-robot relationships.