Global linear stability analysis is performed for a coupled fluid-structure-interaction problem of a NACA0012 airfoil at transitional Reynolds numbers to investigate the phenomenon of spontaneous pitch-oscillations. It is shown that the spontaneous onset of aeroelastic instability is due to a linearly unstable mode of the coupled fluid-structure-interaction problem. The parameter range of instability predicted by the global stability analysis is consistent with the observations of previous experimental and numerical investigations. However, the results show that the onset of instability and the frequency selection mechanisms are decoupled. The onset of pitch-oscillations is caused due to a zero frequency divergence instability while the frequency selection is likely due to a sub critical mode which is non-linearly excited. In addition the stability results provide an explanation for the absence of the von-Karman modes' frequencies in the pitch response, based on the shape of the eigenvectors of the system.