Why is the CASSCF method multi-configurational, while the CI method is not?
When you say multiconfigurational I think you mean that the ground state wavefunction does not have one single dominant MO configuration.

CI can be multiconfigurational depending on the type of excitation included.  For example, Full CI is of course multiconfigurational since it is the exact solution for the basis set used.  However, CIS (single excitations) or CISD (single + double excitations) calculations are the only two CI methods that are computationally efficient enough to be used in practice.  So that’s probably what you mean when you say CI. You also probably mean CIS or CISD based on an RHF wavefunction, to distinguish it from multi-reference CI. 

The lowest energy solution of CIS based on RHF is the RHF energy, so you can think of the SCF procedure as a form of CIS.  

So a CASSCF(2,2) calculation (e.g. where the active space is HOMO, LUMO) is a bit like a CISDT calculation.  For example, there will be contributions to the wavefunction where the LUMO is doubly occupied and another MO outside the active space is “singly excited”.  Thus, the LUMO is allowed to change when electrons are put into it, which becomes more and more important as the HOMO-LUMO gap decreases.  CISD cannot account for this, so in that sense it is not multiconfigurational.