 Solution

Protonation converts OH into a water leaving group; ionization then gives the diarylmethyl cation. The labeled C-H/D bond is retained, so $k_H/k_D=1.18$ is a normal alpha-secondary kinetic isotope effect, not a primary C-H cleavage effect.

At the labeled carbon, tetrahedral geometry becomes approximately trigonal planar. The associated change in bending vibrations and zero-point energies favors the H isotopologue in a substantially carbocation-like transition state. The two anisyl rings stabilize that cation and make this ionization pathway plausible.