Electron is the source of electric field and changing electric field produce magnetic force, what about particle that can do vice versa? My concern is how come universe favors particles that carry electric charge but not magnetic charge? What prevailing theory can explain this discrepancies?
There is no overriding reason why magnetic charges (monopoles) do not seem to exist. It is straightforward to supplement the known laws of classical electrodynamics with magnetic as well as electric point sources. Moreover, in quantum electrodynamics, the existence of magnetic monopoles would actually solve a known problem, since the presence of magnetic charges would require electric charges to be quantized. As a result, physicists have spent a significant amount of effort searching for isolated magnetic sources.
However, they have never been found. It seems that our universe may simply have electric charges but no magnetic charges, for no deep underlying reason that we know of. The most we can say is that if there are magnetic monopoles that we have not yet seen, the reason is probably that they are very heavy. In many extended theories of particle interactions, there are monopoles, but the monopoles have masses much larger than the masses of the electrically charged particles. They are therefore difficult to produce, except in incredibly energetic interactions or in the early universe, when the temperature was very high.
Electron is the source of electric field and changing electric field produce magnetic force...
The electron is the source of an electric field and the electron is the source of a magnetic dipole moment. Both are for a free electron intrinsic (existing independent from sourrounding influences) properties.
Our observations shows that a particle with two monopolar properties - an electric charge and a magnetic charge not exist. The search of magnetic monopoles is possible only on high energy physics and scales below the subatomic particles. The use of such investigations should be a deeper understanding of the electrons inner structure and the structure of electric and magnetic fields and of photons.
Why can't a particle that carries magnetic charge exist?
Electric fields are the reason for accelerations towards or away from other electric charges. Magnetic fields are the reason for deflection of charges. What should be the reaction of a magnetic monopole to the influence of another magnetic monopol? The same as for electric charges? How then we would differ between them? Why not agree that charges contain a monopolar field and a dipole field?