  Although inflation is a natural candidate to generate the lengths of
coherence of magnetic fields needed to explain current observations, it needs
to break conformal invariance of electromagnetism to obtain significant
magnetic amplitudes. Of the simplest realizations are the kinetically-coupled
theories $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ (or $IFF$ theories). However, these
are known to suffer from electric fields backreaction or the strong coupling
problem. In this work we shall confirm that such class of theories are
problematic to support magnetogenesis during inflationary cosmology. On the
contrary, we show that a bouncing cosmology with a contracting phase dominated
by an equation of state with $p>-\rho/3$ can support magnetogenesis, evading
the {backreaction/strong-coupling problem}. Finally, we study safe
magnetogenesis in a particular bouncing model with an ekpyrotic-like
contracting phase. In this case we found that $f^2(\phi)F^2$-instabilities
might arise during the final kinetic-driven expanding phase for steep ekpyrotic
potentials.
