The galactic magnetic field is usually attributed to an alphaomega-dynamo based on the idea of turbulent mixing and dissipation of the magnetic field with an effective eddy diffusion coefficient of the order of 10(25) cm2 s-1. However, there is no evident way in which the interstellar turbulence can mix the relatively strong mean galactic field on the small scales necessary for resistivity or rapid reconnection to provide such dissipation. We conjecture instead that the cosmic-ray gas provides the dissipation by inflating the field and producing the extended magnetic lobes that form the galactic halo. From there the dynamical rapid reconnection of adjacent lobes carries out both the alpha-effect and field dissipation essential for the existence of the galactic alphaomega-dynamo. The process is described approximately by the conventional dynamo equations, so that the net result is not greatly different from presently available simulations of galactic fields. In short, we propose that the azimuthal field is generated primarily in the gaseous disk, while the alpha-effect is carried out in the galactic halo. Insofar as this picture is correct, it suggests that the dynamos in galaxies are "fast" because of the dynamical reconnection of field where opposite components are pressed together. The theoretical field generation rate falls to zero in the limit of vanishing resistivity, but only as the reciprocal of the logarithm of the Lundquist number. This seems to be the essential ingredient in the dynamos operating in stars and galaxies.