  The isospin splitting of the Dirac mass obtained with the relativistic
Brueckner-Hartree-Fock (RBHF) theory is thoroughly investigated. From the
perspective in the full Dirac space, the long-standing controversy between the
momentum-independence approximation (MIA) method and the projection method on
the isospin splitting of the Dirac mass in asymmetric nuclear matter (ANM) is
analyzed in detail. We find that, the \textit{assumption procedure} of the MIA
method, which assumes that the single-particle potentials are momentum
independent, is not a sufficient condition that directly leads to the wrong
sign of the isospin splitting of the Dirac mass, while the \textit{extraction
procedure} of the MIA method, which extracts the single-particle potentials
from the single-particle potential energy, leads to the wrong sign. By
approximately solving the set of equations involved in the \textit{extraction
procedure}, a formal expression of the Dirac mass is obtained. The wrong
isospin splitting of the Dirac mass is mainly caused by that the
\textit{extraction procedure} forcely assumes the momentum dependence of the
single-particle potential energy to be a quadratic form where the strength is
solely determined by the constant scalar potential.
