  Motivated by the first observation of the double-charm tetraquark
$T_{cc}^+(3875)$ by the LHCb Collaboration, we investigate the nature of
$T_{cc}^+$ as an isoscalar $DD^*$ hadronic molecule in a meson-exchange
potential model incorporated by the coupled-channel effects and three-body
unitarity. The $D^0D^0\pi^+$ invariant mass spectrum can be well-described and
the $T_{cc}^+$ pole structure can be precisely extracted. Under the hypothesis
that the interactions between the heavy flavor hadrons can be saturated by the
light meson-exchange potentials, the near-threshold dynamics of $T_{cc}^+$ can
shed light on the binding of its heavy-quark spin symmetry (HQSS) partner
$D^*D^*$ ($I=0$) and on the nature of other heavy hadronic molecule candidates
such as $X(3872)$ and $Z_c(3900)$ in the charmed-anticharmed systems. The
latter states can be related to $T_{cc}^+$ in the meson-exchange potential
model with limited assumptions based on the SU(3) flavor symmetry relations.
The combined analysis, on the one hand, indicates the HQSS breaking effects
among those HQSS partners, and on the other hand, highlights the role played by
the short and long-distance dynamics for the near threshold $D^{(*)}D^{(*)}$
and $D^{(*)}\bar{D}^{(*)}+c.c.$ systems.
