Thanks, both of these are great explanations. I am offering a heuristic explanation: Any state of the electromagnetic field is characterized by a probability distribution of occupancy of photon number states |m>. Suppose that the state we are looking for has an expected number of photons greater than zero. During absorption, photons are removed from every state that has photons in it. There is also, in general, a finite probability that the electromagnetic field is in the state with no photons |0>. When we remove a photon, owing to the distributed probability of the state of the EM field we have a finite probability of reducing the number of photons in any number state including the state with zero photons. If the EM field happens to have no photons, nothing happens, we do not get a photon and this is not a problem: the expected number of photons in the state is still reduced by one owing to the distributed probability of population in states with number of photons greater than zero. Hence, there is no reason why the resulting state could not have a continuous probability distribution albeit corresponding to one photon less, namely, the state should be an eigenstate of the annihilation operator. However, if one tries adding a photon to such a state, it will be impossible to ever alter or contribute to the probability of eigenstate |0> and therefore it will be impossible, but adding a photon, to reconstruct a probability distribution we started from, namely, the state we are looking for is not an eigenstate of the creation operator.