Twinning is profuse in bcc transition metals (TMs) except bulk W and Mo. However, W and Mo nanocrystals surprisingly exhibit twinning during room temperature compression, which is completely unexpected as established nucleation mechanisms are not viable in them. Here, we reveal the physical origin of deformation twinning in W and Mo. We employ density functional theory (DFT) and a reduced-constraint slip method to compute the stress-dependent generalized stacking fault enthalpy (GSFH), the thermodynamic quantity to be minimized under constant loading. The simple slipped structures and GSFH lines show that compressive stresses stabilize a two-layer twin embryo, which can grow rapidly via twinning disconnections with negligible energy barriers. Direct atomistic simulations unveil the explicit twinning path in agreement with the DFT GSFH lines. Twinning is thus the preferred deformation mechanism in W and Mo when shear stresses are coupled with high compressive stresses. Furthermore, twinnability can be related to the elastic constants of a stacking fault phase (SFP). The hcp phase may serve as a candidate SFP for the {112}⟨1[over ¯]1[over ¯]1⟩ twinning system in bcc TMs and alloys, which is coincident with the {111}⟨112[over ¯]⟩ twinning in fcc structures.