The existence of negative ions in interstellar clouds has been associated for several decades with the process of radiative electron attachment. In this Letter, we report compelling evidence supporting the fact that the radiative attachment of a low-energy electron is inefficient to form the carbon chain anions CN^{-}, C_{3}N^{-}, and C_{5}N^{-} detected in interstellar clouds. The validity of the approach is confirmed by good agreement with experimental data obtained for the inverse photodetachment process, which represents the major cause of anion destruction in interstellar space. As a consequence, we suggest alternative models that could explain the formation of anions.