  Although asymptotic freedom is an essential feature of QCD, it is absent in
effective chiral quark models like the Nambu--Jona-Lasinio and linear sigma
models. In this work we advocate that asymptotic freedom plays a key role in
the recently observed discrepancies between results of lattice QCD simulations
and quark models regarding the behavior of the pseudocritical temperature
$T_{\rm pc}$ for chiral symmetry restoration in the presence of a magnetic
field $B$. We show that the lattice predictions that $T_{\rm pc}$ decreases
with $B$ can be reproduced within the Nambu--Jona-Lasinio model if the coupling
constant $G$ of the model decreases with $B$ and the temperature. Without
aiming at numerical precision, we support our claim by considering a simple
ansatz for $G$ that mimics the asymptotic freedom behavior of the QCD coupling
constant $1/\alpha_s \sim \ln (eB/\Lambda^2_{QCD})$ for large values of $B$.
