We present high resolution spectroscopy of the common proper motion system FH Leo (components HD 96273 and BD+07 2411B), which has been classified as a novalike variable due to an outburst observed by Hipparcos, and we present and review the available photometry. We show from our spectra that neither star can possibly be a cataclysmic variable, instead they are perfectly normal late-F and early-G stars. We measured their radial velocities and derived the atmospheric fundamental parameters, abundances of several elements including Fe, Ni, Cr, Co, V, Sc, Ti, Ca and Mg, and we derive the age of the system. From our analysis we conclude that the stars do indeed constitute a physical binary. However, the observed outburst cannot be readily explained. We examine several explanations, including pollution with scattered light from Jupiter, binarity, microlensing, background supernovae, interaction with unseen companions and planetary engulfment. While no explanation is fully satisfactory, the scattered light and star-planet interaction scenarios emerge as the least unlikely ones, and we give suggestions for further study.