A strong enhancement at low γ-ray energies has recently been discovered in the γ-ray strength function of ^{56,57}Fe. In this work, we have for the first time obtained theoretical γ decay spectra for states up to ≈8 MeV in excitation for ^{56,57}Fe. We find large B(M1) values for low γ-ray energies that provide an explanation for the experimental observations. The role of mixed E2 transitions for the low-energy enhancement is addressed theoretically for the first time, and it is found that they contribute a rather small fraction. Our calculations clearly show that the high-ℓ(=f) diagonal terms are most important for the strong low-energy M1 transitions. As such types of 0ℏω transitions are expected for all nuclei, our results indicate that a low-energy M1 enhancement should be present throughout the nuclear chart. This could have far-reaching consequences for our understanding of the M1 strength function at high excitation energies, with profound implications for astrophysical reaction rates.