1. Atoms absorb only certain frequencies as well. In an emission experiment (i.e., in an ICP-AES, or a star perhaps), the energy source incident to an atomized sample is generally a continuum. Excited atoms only emit certain ones, as do ground state atoms undergoing absorption events. It is possible to absorb a high energy photon and emit lower energy photons. This is more common in molecules, which convert some of the absorbed energy into heat, which accounts for the difference. In gas phase atoms, the absorbing and emitting states are more or less the same, as there is no significant structural relaxation in the excited state.
2. The point is that you don't see continuum emission (white light, or light of all wavelengths) from gas phase atoms, because electrons exist in discrete energy states. You can certainly generate a continuum of light - for example, the heated tungsten filament in a conventional light bulb does a reasonably good job of this - but the process of photon generation is completely different from what's going on in emission from a gas-phase sample of atoms.