  The standard galaxy formation theory assumes that baryons and dark matter are
initially well-mixed before becoming segregated due to radiative cooling. We
use non-radiative hydrodynamical simulations to explicitly examine this
assumption and find that baryons and dark matter can also be segregated because
of different physics obeyed by gas and dark matter during the build-up of the
halo. As a result, baryons in many haloes do not originate from the same
Lagrangian region as the dark matter. When using the fraction of corresponding
dark matter and gas particles in the initial conditions (the "paired fraction")
as a proxy of the dark matter and gas segregation strength of a halo, on
average about $25$ percent of the baryonic and dark matter of the final halo
are segregated in the initial conditions. This is at odds with the assumption
of the standard galaxy formation model. A consequence of this effect is that
the baryons and dark matter of the same halo initially experience different
tidal torques and thus their angular momentum vectors are often misaligned. The
degree of the misalignment is largely preserved during later halo assembly and
can be understood with the tidal torque theory. The result challenges the
precision of some semi-analytical approaches which utilize dark matter halo
merger trees to infer properties of gas associated to dark matter haloes.
