Type I binary-induced supernovae do not leave behind rotating neutron stars.
Pulsars spin down and become too faint to observe after several tens of millions of years.
Type II core-collapse supernovae do not leave behind rotating neutron stars.
The radiation responsible for a typical pulsar "blip" leaves the neutron star in narrow beams, which we can only detect if our line of sight is crossed by them.
No selection of an incorrect statement from among these can be made, since they are all true.