We report the nonreciprocal excitation of propagating forward volume exchange spin waves in yttrium iron garnet (YIG) thin film with perpendicular anisotropy by bringing the in-plane magnetization of Co20Fe60B20 (CoFeB) nanowires to resonance. All-electric spin-wave spectroscopy is used to measure propagating spin waves in YIG subjected to out-of-plane external magnetic fields. The nonreciprocity can be reconfigured by inverting the in-plane magnetization of the CoFeB nanowires. The exchange spin waves achieved in the experiments have wavelengths down to about 150 nm and fast group velocities of up to 1.6 km/s, which can be accounted for with the dipole-exchange spin-wave dispersion of the forward volume mode. Micromagnetic simulations reproduce these experimental features, verifying that the key physics behind this nonreciprocity is the intrinsically chiral dynamic stray fields generated by the resonating CoFeB magnetization. Our results provide key insights into advanced and high-frequency magnonic devices.