  Recently entanglement suppression was proposed to be one possible origin of
emergent symmetries. Here we test this conjecture in the context of heavy meson
scatterings. The low-energy interactions of $D^{(*)}\bar D^{(*)}$ and $D^{(*)}
D^{(*)}$ are closely related to the hadronic molecular candidates $X(3872)$ and
$T_{cc}(3875)^+$, respectively, and can be described by a nonrelativistic
effective Lagrangian manifesting heavy-quark spin symmetry, which includes only
constant contact potentials at leading order. We explore entanglement
suppression in a tensor-product framework to treat both the isospin and spin
degrees of freedom. Using the $X(3872)$ and $T_{cc}(3875)^+$ as inputs, we find
that entanglement suppression indeed leads to an emergent symmetry, namely, a
light-quark spin symmetry, and as such the $D^{(*)}\bar D^{(*)}$ or $D^{(*)}
D^{(*)}$ interaction strengths for a given total isospin do not depend on the
total angular momentum of light (anti)quarks. The $X(3872)$ and
$T_{cc}(3875)^+$ are predicted to have five and one isoscalar partner,
respectively, while the corresponding partner numbers derived solely from
heavy-quark spin symmetry are three and one, respectively. The predictions need
to be confronted with experimental data and lattice quantum chromodynamics
results to further test the entanglement suppression conjecture.
