Basicly, there are no explanation of why they spin and what causes spin. The only we know about spin of elementary particles - that it can not be arbitrary value (but only certain quantisied values), and that it conserves in all particle interactions - in full agreement with angular momentum conservation law.

Spin and associated with it magnetic field indicates that elementary particles have inner structure. Most scientists believe that this structure is likely to be very small - of order of Plank scale. And all elementary particles have identical (or similar) structure but different inner motion in this structure. The result of this motion is what we see as mass, charge, spin, baryon charge, strangeness, etc.