We discuss the fate of chiral symmetry in an extremely strong magnetic field B. We investigate not only quark fluctuations but also neutral meson effects. The former would enhance the chiral-symmetry breaking at finite B according to the Magnetic Catalysis, while the latter would suppress the chiral condensate once B exceeds the scale of the hadron structure. Using a chiral model we demonstrate how neutral mesons are subject to the dimensional reduction and the low dimensionality favors the chiral-symmetric phase. We point out that this effect, the Magnetic Inhibition, can be a feasible explanation for recent lattice-QCD data indicating the decreasing behavior of the chiral-restoration temperature with increasing B.

5 pages, 2 figures