Pulsar-white dwarf binary

In the paper from Hulse & Taylor 1975 on the first discovery of a pulsar in a binary system, they conclude that the companion to the pulsar must be

a compact object, probably a neutron star or black hole. A white dwarf companion cannot be ruled out, but seems unlikely for evolutionary reasons.

My question is why is a white dwarf companion unlikely, given that we have observed pulsar-white dwarf binary systems (e.g. PSR J1141-6545).

Thanks