Spin can be derived as an entity that is intimately related to the symmetries of spacetime. In flat Minkowski spacetime the symmetry seems to be the SO(3,1) Lorentz group. But one can enlarge this symmetry via complexification to SL(2,C) and show that this is locally isomorphic to two copies of SU(2)*SU(2). This is the reason why in 4-component Dirac spinors we have two two-component spinors (large and small component). Therefore integer and half-integer spin follow rather naturally from the symmetry group of (flat Minkowski) spacetime.
Constructing a theory of gravity coupled to spin-half fields it becomes clear that this is not possible by using the metric formalism; one must enlarge the formalism to so-called tetrads. These are something like basis vectors of a four-dim. tangent space attached to each point in spacetime. Using these tangent spaces one can "gauge" the Lorentz symmetry, i.e. one can introduce a local SL(2,C) gauge symmetry. This gauge symmetry means that one can rotate the tetrads at each spacetime differently b/c there is a connection, a gauge-field so to speak, which plays a similar role as a gauge field in ordinary gauge theories: it compensates the effect of local gauge transformations and makes the theory gauge invariant (this symmetry and the gauge field is not visible in the metric formalism).
b/c of this local SL(2,C) gauge symmetry one can say that locally a curved Riemann manifold = spacetime has the same symmetry structure as flat Minkowski space and that this allows for the same construction of spinor fields as in Minkowski spacetime.
However there may be a global obstruction to introducing spin. A Riemann manifold that allows for a spin structure, i.e. the introduction of spinor fields, must have a certain property: it must be orientable (a Möbius strip isn't orientable) and its second Stiefel-Whitney class must vanish (unfortunately I cannot explain lucidly what this means). Therefore not all Riemann manifolds allow for the construction of spinor fields.
Assuming that the topology of spacetime remains invariant during expansion (time evolution) of the universe (which is the case in general relativity except for the formation of black holes) the spin structure does not change. It's a topological invariant.
The relation to the standard model is simply the fact that our universe allows for a spin structure and that therefore a plethora of elementary particles with spin (spin 1/2) can exist. The different particle species (electron, quarks, neutrinos, ...) in the standard model cannot be restricted or derived from the symmetry structure of spacetime. All what we can say is that spin 1/2 seems to exist and that we have a mathematical classification of manifolds which allow for spin to exist.
