A few years ago, it was claimed that the two-dimensional ferromagnetic planar Hf monolayer could be synthesized on Ir(111). However, several questions remained unanswered. Herein, we unravel the structural stability of the HF monolayer and its influence on magnetism using first principles calculations. Despite the ferromagnetic state in the planar free-standing Hf layer, extensive systematic calculations with phonon spectra reveal that the planar free-standing Hf layer is unstable and it has a non-magnetic high-buckled structure in the ground state. We also find a structural transition from buckled to flat honeycomb geometry on the Ir(111) substrate. Nonetheless, 2D hafnene has no magnetic state due to strong hybridization with the Ir(111) surface. The evolution from the non-magnetic to the ferromagnetic state combined with structural transition is observed by adding BN as a spacer layer on the Ir(111) substrate (BN/Ir(111)). In addition, we find that 2D Hf on BN/Ir(111) has a giant perpendicular magnetic anisotropy of 3.41 meV.