Because the mechanism that facilitates the 'pulsing' is the rotation of the object. This is the only mechanism anyone has ever been able to propose that accounts for the unbelievable regularity of the pulses. A white dwarf is about the size of the Earth some 10,000 kilometers in diameter, with a circumference of about 30,000 kilometers. For such an object to be spinning at one rotation every second, which is the typical pulse rate, it would have to be spinning at a speed of 30,000 kilometers per second. It would shatter under these centrifugal forces. Only neutron stars are compact enough, about 15 kilometers in radius, that they can rotate fast enough without breaking up.