They are saying that since we don't find transitional forms, evolution could not have occurred slowly and gradually, so obviously, then, it must have occurred rapidly. How and why evolution occurs so rapidly, no one knows. As a matter of fact, the idea that multiplied millions of rapid bursts of evolution have occurred is contrary to the science of modern genetics. The genetic apparatus of a lizard, for example, is totally devoted to producing another lizard. The idea that by some random evolutionary process the genetic apparatus of a lizard could be rapidly reorganized to produce something really significantly different is clearly contrary to everything we know.
Evolutionists simply have no mechanism for evolution.
Secondly, the notion of punctuated equilibrium doesn't solve the really serious problem evolutionists have with the fossil record. In fact, it doesn't even address that problem. The idea of punctuated equilibrium was invented to explain the lack of transitional forms between species. But that is not the real problem. The really serious problem is the absence of transitional forms between the higher categories, that is, between families, orders, classes and phyla.