Why are the fan blades mounted loosely?
The blades are loose in their "Fir Tree" blade mounts so that they can self balance. They are called "fir tree" because they are v shaped.   

As the rotation speed and centrifugal force increases, they move in the mounts and establish individual lead/lag positions to achieve a balanced disc. 


  It will be understood that turbine wheels rotate at very high speeds
  of rotation, thereby generating large centirfugal forces tending to
  throw the blades outwardly from the wheel. By providing contact
  surfaces of equal and opposite slope with respect to the longitudinal
  axis of the root on opposite sides of root, the force components of
  the centrifugal force balance each other out. Periodic and other
  vibrations which might otherwise be generated are damped out and
  greatly minimized


Source: Fir tree blade mount Patent