why do we relate spin with angular momentum operator in quantum mechanics? In fact angular momentum is the generator of rotation around an axis.
If the axis passes through the center of mass of the object then it is spinning.
spin in QM can be a property of point particle(such as electron) that can't rotate around it self.
 A: The main reason is that in the first two decades of XXth century, physicists discovered experimentally that some systems (in particular, silver atoms) reacted to magnetic fields in a way which was not explainable by means of current physics, i.e. instead of being spatially deflected by a magnetic field in a continuous fashion, they condensed in two discrete spots on the revelator screen.
After unsuccessfully trying to explain the phenomenon by means of the only angular momentum known at that time, the orbital one, physicists introduced a new internal degree of freedom, which is currently the well known “spin”, and because of its nature (i.e. reaction to a magnetic field) it is associated to angular momentum.
A: The simplest answer is "conservation of angular momentum". It is a very strict conservation law both in classical and quantum mechanics.
In interactions of elementary particles which have to be described in the framework of quantum mechanics, since the 1960's a large number of observations were modeled with the standard model of physics.. The spins were assigned to the elementary particles so that angular momentum would be conserved during their interactions. 
The eightfold way , which pointed to the existence of the quarks with their half integer spin, is based on assuming angular momentum conservation in the data gathered over the decays. The model is successful and predictive, so the assignement of spins to the elementary particles is considered to be based on experimental observations.
One familiar with nuclear and atomic physics could make similar arguments for the periodic table and the spectra of atoms.The spins used in the models  to the electrons and the  nuclei fit the data and the models are predictive.
Here is a historical review of electron spin,.
