  In this work we revisit itinerant ferromagnetism in 2D and 3D electron gases
with arbitrary spin-orbit splitting and strong electron-electron interaction.
We identify the resonant scattering processes close to the Fermi surface that
are responsible for the instability of the ferromagnetic quantum critical point
at low temperatures. In contrast to previous theoretical studies, we show that
such processes cannot be fully suppressed even in presence of arbitrary
spin-orbit splitting. A fully self-consistent non-perturbative treatment of the
electron-electron interaction close to the phase transition shows that these
resonant processes always destabilize the ferromagnetic quantum critical point
and lead to a first-order phase transition. Characteristic signatures of these
processes can be measured via the non-analytic dependence of the spin
susceptibility on magnetic field both far away or close to the phase
transition.
