The spin-orbit interaction generally leads to spin splitting (SS) of electron and hole energy states in solids, a splitting that is characterized by a scaling with the wave vector k. Whereas for 3D bulk zinc blende solids the electron (heavy-hole) SS exhibits a cubic (linear) scaling with k, in 2D quantum wells, the electron (heavy-hole) SS is currently believed to have a mostly linear (cubic) scaling. Such expectations are based on using a small 3D envelope function basis set to describe 2D physics. By treating instead the 2D system explicitly as a system in its own right, we discover a large linear scaling of hole states in 2D. This scaling emerges from coupling of hole bands that would be unsuspected by the standard model that judges coupling by energy proximity. This discovery of a linear Dresselhaus k scaling for holes in 2D implies a different understanding of hole physics in low dimensions.