Why is no dynamical correlation recovered in the CASSCF method?
The difference between dynamical and static correlation has always been ill-defined, and there is no clear-cut delineation between them.

Correlation simply means that the probability of finding an electron somewhere at position $a$ and another electron somewhere at position $b$ is not simply the product of the two probabilities.

(In that respect, even Hartree-Fock has some correlation since it forbids two same spin electrons occupying the same state (Fermi correlation).)

Correlation was originally thoguht of as the instantaneous repulsion of electrons. This was dynamic correlation. The origin of the difference between static and dynamical correlation came from studies of bond dissociation in molecules. As you pull a bond apart, the electrons should be further apart, and correlation energy should decrease. However, the opposite was found, and in many cases the correlation energy increases. Therefore, there must be some sort of "other" correlation occurring. This was static correlation.

This is because there are additional (near-)degenerate configurations that contribute strongly to the nature of the wave function during dissociation. You can think of this as a manifestation of entanglement, of which Hartree-Fock, being single determinant, fails miserably.

In short, static correlation came to describe situations where the underlying Hartree-Fock reference was a qualitative and quantitative failure. 

Dynamic correlation, on the other hand, was used to describe the cases where the underlying Hartree-Fock reference has the correct qualitative behavior, but was not quantitatively accurate.

CASSCF does a better job at calculating static correlation because most of the important near degenerate configurations are multi-electron excitations within a small valence space. Thus it generally captures the configurations necessary to describe bond breaking, etc. with a well-chosen active space.

Single reference coupled cluster, does better at capturing dynamic correlation because it is usually truncated to few-pair excitations, like the double excitations of CCSD, but cover the whole virtual space.

For high levels of coupled cluster, e.g. CCSDTQ, the distinction between static and dynamic correlation really breaks down, and some high level coupled cluster calculations actually do quite a good job at otherwise "multireference problems." Multireference coupled cluster --- combining the best of CASSCF and CC --- is an active area of research today.