The beam bending theory is only an approximation of real 2D theory of elasticity in the case of relatively slender bodies, therefore it does not predict such local effects as infinite stresses caused by concentrated loads. On the other hand, FE modeling also gives only approximate result, which is expected to converge to exact solution of 2D theory of elasticity with mesh refinement.

Theoretical Solution is based on the concept of pure bending that's why it does not meet with FEA solution. Apply only moment instead of point load to match your result.

The problem is that you apply concentrated load to the beam modeled by 2D finite elements, which means that, in essence, you deal with equations of 2D theory of elasticity. In this case, according to the exact solution, stresses in the vicinity of the loaded point tend to infinity. You can see this effect by refining the mesh in your model. At some remote points, however, the FE results should agree with the solution based on the beam theory. For example, the tensile stresses at the lower surface of the beam are in good agreement.

For comparison, you could consider the beam under uniformly distributed load. The results would be more optimistic.