We analyze the role of multielectron dynamics in high-harmonic generation spectroscopy, using an example of a two-electron system. We identify and systematically quantify the importance of correlation and exchange effects. One of the main sources for correlation is identified to be the polarization of the ion by the recombining continuum electron. This effect, which plays an important qualitative and quantitative role, seriously undermines the validity of the standard approaches to high-harmonic generation, which ignore the contribution of excited ionic states to the radiative recombination of the continuum electron.