The stabilisation problem of second-order switched positive systems consisting of two unstable subsystems is considered in this article. By considering the vector fields and geometric characteristics, a necessary and sufficient condition for the stabilisability of second-order switched positive systems with two unstable subsystems is provided. Furthermore, it is shown via this condition that neither second-order switched positive systems consisting of two subsystems with unstable nodes nor second-order switched positive systems consisting of one subsystem with unstable nodes and the other with a saddle point can be stabilised via any switching law.