Why are quasars small?
They are not.
Quasars are the accretion disks of massive black holes. Essentially all the matter that was attracted by the gravity of the black hole, that did not cross the Schwarzschild radius (essentially the point where nothing escapes), is in orbit of the black hole in the quasar. As such the quasar can be imagined to be a disk of solid matter, a trillion times (or more) brighter than our sun and around a light year across.
Imagine our solar system out to one light year. Now imagine a disk with a hole at the center. The edge of the disc starts about 1/4 of the way from the sun to Mercury. Then you go out passed the Kuiper belt to the edges of the inner oort cloud. That is about 1 light year.
Now take about 200,000,000 suns and cram them all into that space. This should give you an idea of the mass and size of a quasar. I cannot imagine anyone describing this as small.
Could you have meant pulsar?