  We explain in simple terms how the buildup of dark haloes by merging compact
satellites, as in the CDM cosmology, inevitably leads to an inner cusp of
density profile $\rho \propto r^{-\alpha}$ with $\alpha \gsim 1$, as seen in
cosmological N-body simulations. A flatter halo core with $\alpha <1$ exerts on
the satellites tidal compression in all directions, which prevents deposit of
stripped satellite material in the core region. This makes the satellite orbits
decay from the radius where $\alpha \sim 1$ to the halo centre with no local
tidal mass transfer and thus causes a rapid steepening of the inner profile to
$\alpha >1$. These tidal effects, the resultant steepening of the profile to a
cusp, and the stability of this cusp to tandem mergers with compact satellites,
are demonstrated using N-body simulations. The transition at $\alpha \sim 1$ is
then addressed using toy models in the limiting cases of impulse and adiabatic
approximations and using tidal radii for satellites on radial and circular
orbits. In an associated paper we address the subsequent slow convergence from
either side to an asymptotic stable cusp with $\alpha \gsim 1$. Our analysis
thus implies that an inner cusp is enforced when small haloes are typically
more compact than larger haloes, as in the CDM scenario, such that enough
satellite material makes it intact into the inner halo and is deposited there.
We conclude that a necessary condition for maintaining a flat core, as
indicated by observations, is that the inner regions of the CDM satellite
haloes be puffed up by about 50% such that when they merge into a bigger halo
they would be disrupted outside the halo core. This puffing up could be due to
baryonic feedback processes in small haloes, which may be stimulated by the
tidal compression in the halo cores.
