  By comparing the two- and three-flavor Nambu--Jona-Lasinio (NJL) models, we
demonstrate that the naively expected vacuum superconductivity (VSC) in
constant magnetic field ${\bf B}=B\hat z$ is disfavored due to the splitting
magnetic catalysis effect (MCE) to chiral condensates with different quark
flavors. Based on the simple two-flavor NJL model, we illuminate, in the lowest
Landau level approximation, the similar origins of $\pi^0$ and $\bar{\rho}^+_1$
(${\rho}^+$ meson with spin $S_z=1$) mass reductions with smaller $B$ and their
different features at larger $B$. With the full Landau levels, the two-flavor
NJL model is found to be invalid to study the magnetic field effect to
$\bar{\rho}^+_1$ meson with physical vacuum mass $775~{\rm MeV}$. Then,
restricted to $\rho$ meson mass below two-quark threshold in vacuum, that is
$m_\rho^v<2m_q^v$, it is found that $\pi^0$ mass decreases and then increases
with $B$ slowly, and $\bar{\rho}^+_1$ mass vanishing point is delayed to larger
$B$ compared to the point particle result. In the more realistic three-flavor
NJL model, all the quark masses split in strong magnetic field as a
combinatorial result of their different current masses and electric charges. By
choosing a vacuum mass closer to the physical one, $\bar{\rho}^+_1$ meson mass
is found to be consistent with the LQCD results semi-quantitatively in smaller
$B$ region but increase in larger $B$ region. These features are mainly
outcomes of the interplay between the $S_z-B$ coupling effect and splitting MCE
to the composite $u$ and $d$ quarks, which definitely disfavors VSC when the
latter dominates. Furthermore, mesonic flavor mixing is modified by $B$ among
the neutral pseudoscalars: $\pi^0,\eta_0$ and $\eta_8$, which is very important
to suppress the mass enhancement of the effective mass eigenstates at large
$B$.
