The importance of the magnetic field in the high-mass star formation regime is a long-standing question. Several observational properties in high-mass star-forming regions are frequently "explained" invoking magnetic fields, despite the lack of direct evidence of their presence or their importance with respect to gravity and turbulence. We introduce here the first ALMA survey, Magnetic Fields in Massive Star-forming Regions (MagMaR). In MagMaR, 30 high-mass star-forming regions have been observed at 1.2 mm, resulting in ~0.3" resolution (~1000 au). A large variety of B-field morphologies is detected: (1) spiral- or hourglass-like, that are dominated by a single, bright continuum source; (2) filamentary, with a magnetic field sometimes parallel to the filamentary dust emission and characterized by aligned fragmentation; (3) complex magnetic field morphology with highly clustered fragmentation. Here we present the case study of IRAS 18089-1732. The dust continuum emission and magnetic field morphology present spiral-like features resembling a whirlpool. The modeled magnetic field corresponds to a weakly magnetized core, having a toroidal component that is 30% in strength of the poloidal component. Using the DCF method, we estimate a magnetic field strength of 3.5 mG. The energy balance of the system at ~1000 au scales indicates that gravity overwhelms turbulence, rotation, and the magnetic field. We therefore conclude that high-mass star formation can occur in weakly magnetized environments, with gravity taking the dominant role.