  Recently the EDGES collaboration reported an anomalous absorption signal in
the sky-averaged 21-cm spectrum around $z=17$. Such a signal may be understood
as an indication for an unexpected cooling of the hydrogen gas during or prior
to the so called Cosmic Dawn era. Here we explore the possibility that dark
matter cooled the gas through velocity-dependent, Rutherford-like interactions.
We argue that such interactions require a light mediator that is highly
constrained by 5th force experiments and limits from stellar cooling.
Consequently, only a hidden or the visible photon can in principle mediate such
a force. Neutral hydrogen thus plays a sub-leading role and the cooling occurs
via the residual free electrons and protons. We find that these two scenarios
are strongly constrained by the predicted dark matter self-interactions and by
limits on millicharged dark matter respectively. We conclude that the 21-cm
absorption line is unlikely to be the result of gas cooling via the scattering
with a dominant component of the dark matter. An order 1\% subcomponent of
millicharged dark matter remains a viable explanation.
