Repulsive short-range interactions can induce p-wave attraction between fermions in dense matter and lead to Cooper pairing at the Fermi surface. We investigate this phenomenon, well-known as the Kohn-Luttinger effect in condensed matter physics, in dense matter with strong short-range repulsive interactions. We find that repulsive interactions required to stabilize massive neutron stars can induce p-wave pairing in neutron and quark matter. When massive vector bosons mediate the interaction between fermions, the induced interaction favors Cooper pairing in the 3P2 channel. For the typical strength of the interaction favored by massive neutron stars, the associated pairing gaps in neutrons can be in the range of 10 keV to 10 MeV. Strong and attractive spin-orbit and tensor forces between neutrons can result in repulsive induced interactions that greatly suppress the 3P2 pairing gap in neutron matter. In quark matter, the induced interaction is too small to result in pairing gaps of phenomenological relevance.