Spin-coupled [SC(8)/6-31G(d,p)] calculations on top of the MP2/6-31G(d,p) intrinsic reaction coordinate are used in order to obtain a model for the electronic mechanism of the gas-phase concerted 1,3-dipolar cycloaddition (13DC) reaction between methyl azide (CH3N3) and ethene (C2H4). It is shown that this reaction follows a homolytic mechanism characterized by an almost simultaneous breaking of the two coplanar pi bonds in methyl azide and of the T bond in ethene, and the subsequent reengagement of the valence orbitals initially responsible for these bonds into two new bonds, closing the triazole ring, and a lone pair on the central nitrogen in the product. This is in contrast to previous SC research which established heterolytic mechanisms, realized through the movement of electron pairs, for 13DC reactions involving 1,3-dipoles with more polar coplanar pi bonds, such as fulminic acid (HCNO) and diazomethane (CH2N2). We find that neither the homolytic nor heterolytic mechanisms for 13DC reactions involve aromatic transition states. Other aspects of the gas-phase concerted 13DC reaction of methyl azide with ethene, including optimized transition structure geometry, electronic activation energy, activation barrier corrected for zero-point energies, and standard enthalpy, entropy, and Gibbs free energy of activation, have been calculated at the HF/6-31G(d), HF/6-31G(d,p), B3LYP/6-31G(d), B3LYP/6-31G(d,p), MP2/6-31G(d), MP2/6-31G(d,p), QCISD/6-31G(d), and CCD/6-31G(d) levels of theory. The paper includes a critical survey of recently published research on the electronic mechanisms of 13DC reactions and reveals the limitations of approaches relying on closed-shell wave functions and/or on hand-crafted valence-bond constructions.