N-doped SrO seems to be one of the model systems for d^0 magnetism, in which magnetism (or ideally, ferromagnetism) was ascribed to the localized N 2p spins mediated by delocalized O 2p holes. Here we offer a different view, using density functional calculations. We find that N-doped SrO with solely substitutional N impurities as widely assumed in the literature is unstable, and instead that a pairing state of substitutional and interstitial N impurities is significantly more stable and has a much lower formation energy than the former by 6.7 eV. The stable (N_{sub}-N_{int})^{2-} dimers behave like a charged (N_2)^{2-} molecule and have each a molecular spin=1. However, their spin-polarized molecular levels lie well inside the wide band gap of SrO and thus the exchange interaction is negligibly weak. As a consequence, N-doped SrO could not be ferromagnetic but paramagnetic.