Neutron stars form from the collapsed cores of massive stars in supernova explosions. DNS systems are rare because the formation of such a binary system requires it to survive two supernova explosions. PSR J1930-1852 is likely to have formed before its companion star went supernova. During that time, it accreted material from its companion star and spun-up. This process of accretion and spin-up is known as recycling. However, for PSR J1930-1852, the recycling process was shorter than average in duration and/or inefficient. The companion star went supernova before PSR J1930-1852 spun-up sufficiently.
Swiggum et al. (2015), “PSR J1930-1852: a pulsar in the widest known orbit around another neutron star”, arXiv:1503.06276 [astro-ph.HE]