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We analyze the problem of neutrino oscillations via a fermionic particle detector model inspired by the physics of the Fermi theory of weak interactions. The model naturally leads to a description of emission and absorption of neutrinos in terms of localized two-level systems. By explicitly including source and detector as part of the dynamics, the formalism is shown to recover the standard results for neutrino oscillations without mention to "flavor states," which are ill defined in quantum field theory. This illustrates how particle detector models provide a powerful theoretical tool to approach the measurement issue in quantum field theory and emphasizes that the notion of flavor states, although sometimes useful, must not play any crucial role in neutrino phenomenology. [ABSTRACT FROM AUTHOR]