In the standard scenario for binary pulsar formation, the neturon star from the explosion of the primary supergiant moves through the envelope of the companion star. The envelope is then expelled through the hydrodynamic coupling of the dynamical friction. With loss of energy, the orbit of the neutron star tightens. In moving through the companion star envelope, then neutron star accretes a substantial amount of matter. Chevalier has estimated that this well generally send the neutron star into a black hole. We are able to confirm his estimates showing that the amount of accretion can be simply related to the energy loss through dynamical friction. This connection shows that if the latter is sufficient to expel the envelope, then the neutron star will accrete greater than or = 1 solar mass, which is sufficient to convert it into a black hole. A new scenario, in which binary pulsars generally result from the explosion of helium star binaries, is suggested. Not only can black hole formation be avoided in this scenario, but it would result in nearly equal masses for the two neutron stars in the binary. There is evidence for this. Statistics of the (rare) binary pulsar formation are discussed.