  Despite a great success of the Skyrme mean-field approach in exploration of
nuclear dynamics, it seems to fail in description of the spin-flip M1 giant
resonance. The results for different Skyrme parameterizations are contradictory
and poorly agree with experiment. In particular, there is no parameterization
which simultaneously describes the one-peak gross structure of M1 strength in
doubly magic nuclei and two-peak structure in heavy deformed nuclei. The reason
of this mismatch could lie in an unsatisfactory treatment of spin correlations
and spin-orbit interaction. We discuss the present status of the problem and
possible ways of its solution. In particular, we inspect i) the interplay of
the collective shift and spin-orbit splitting, ii) the isovector M1 response
versus isospin-mixed responses, and iii) the role of tensor and isovector
spin-orbit interaction.
