Pressure-induced polymerization of aromatic compounds leads to novel materials containing sp3 carbon-bonded networks. The choice of the molecular species and the control of their arrangement in the crystal structures via intermolecular interactions, such as the arene-perfluoroarene interaction, can enable the design of target polymers. We have investigated the crystal structure compression and pressure-induced polymerization reaction kinetics of two polycyclic 1:1 arene-perfluoroarene cocrystals, naphthalene/octafluoronaphthalene (NOFN) and anthracene/octafluoronaphthalene (AOFN), up to 25 and 30 GPa, respectively, using single-crystal synchrotron X-ray diffraction, infrared spectroscopy, and theoretical computations based on density-functional theory. Our study shows the remarkable pressure stability of the parallel arene-perfluoroarene π-stacking arrangement and a reduction of the interplanar π-stacking separations by ca. 19-22% before the critical reaction distance is reached. A further strong, discontinuous, and irreversible reduction along the stacking direction at 20 GPa in NOFN (18.8%) and 25 GPa in AOFN (8.7%) indicates the pressure-induced breakdown of π-stacking by formation of σ-bonded polymers. The association of the structural distortion with the occurrence of a chemical reaction is confirmed by a high-pressure kinetic study using infrared spectroscopy, indicating one-dimensional polymer growth. Structural predictions for the fully polymerized high-pressure phases consisting of highly ordered rods of hydrofluorocarbons are presented based on theoretical computations, which are in excellent agreement with the experimentally determined unit-cell parameters. We show that the polymerization takes place along the arene-perfluoroarene π-stacking direction and that the lateral extension of the columns depends on the extension of the arene and perfluoroarene molecules.