Context. Understanding the launching mechanism of winds and jets remains one of the fundamental challenges in astrophysics. The Protostellar Outflows at the EarliesT Stages (POETS) survey has recently mapped the 3D velocity field of the protostellar winds in a sample (37) of luminous young stellar objects (YSOs) at scales of 10–100 au via very long baseline interferometry (VLBI) observations of the 22 GHz water masers. In most of the targets, the distribution of the 3D maser velocities can be explained in terms of a magnetohydrodynamic (MHD) disk wind (DW). Aims. Our goal is to assess the launching mechanism of the protostellar wind in the YSO IRAS 21078+5211, the most promising MHD DW candidate from the POETS survey. Methods. We have performed multi-epoch Very Long Baseline Array (VLBA) observations of the 22 GHz water masers in IRAS 21078+5211 to determine the 3D velocities of the gas flowing along several wind streamlines previously identified at a linear resolution of ~1 au. Results. Near the YSO at small separations along (xl ≤ 150 au) and across (R ≤ 40 au) the jet axis, water masers trace three individual DW streamlines. By exploiting the 3D kinematic information of the masers, we determined the launch radii of these streamlines with an accuracy of ~1 au, and they lie in the range of 10–50 au. At increasingly greater distances along the jet (110 au ≤ xl ≤ 220 au), the outflowing gas speeds up while it collimates close to the jet axis. Magneto-centrifugal launching in a radially extended MHD DW appears to be the only viable process to explain the fast (up to 60 km s−1) and collimated (down to 10°) velocities of the wind in correspondence with launch radii ranging between 10 and 50 au. At larger separations from the jet axis (R ≥ 100 au), the water masers trace a slow (≤20 km s−1), radially expanding arched shock-front with kinematics inconsistent with magneto-centrifugal launching. Our resistive-magnetohydrodynamical simulations indicate that this shock-front could be driven by magnetic pressure. Conclusions. The results obtained in IRAS 21078+5211 demonstrate that VLBI observations of the 22 GHz water masers can reliably determine the launching mechanism of protostellar winds.