Why does an electron or proton posses the property of a charge?

Question

If seen, every property is caused due to some reason (eg: solids are hard due to strong force of attraction between its constituents particles), similarly what causes an electron or proton to posses charge?

Answer 1

According to the standard model, the physics of the fields that describe particles: electrons and protons (or, at a lower level, quarks), should not change under an arbitrary local change of phase ("local gauge invariance") - and the mathematical consequences of this requirement are the existence of the photon ("gauge boson") and that the particle field interacts with the photon field with some constant strength, which is the charge.

So the SM says that particles have (electromagnetic) charges. It does not say what the value of that charge will be, it's completely arbitrary (and might be zero). You can wriggle out of that by saying well, it is what it is - but the SM also does not explain why the electron charge and the proton charge have equal magnitude: that's a really big question which Grand Unified theories have tried and failed to answer.

And that leads to the question 'Yes, but why local gauge invariance...?' but please don't ask, as that sequence has no ending.

Answer 2

People first observed and defined charge by studying rubbing stuff together so it produced an attraction or repulsion , sparks produced etc. They had no notion of what the atoms were. The electric and magnetic observations, by the time of Maxwell had solidified into laws that were necessary in order to model charged and magnetic interactions, which finally were mathematically modeled by Maxwell.

Two kinds of charges were known by the 1700 hundreds, called positive and negative. The electron as a single particle observation happened in 1859 , etc. see the history in the link.

The discovery of the proton came in the beginning of the 20th century.

Then came observations that could not be fitted with the classical mathematical theories of Newtonian mechanics and Maxwell's equations, which brought us to the age of quantum mechanics and particle physics.

That the proton and the electron have equal and opposite charge was a fact measured in laboratory experiments. The standard model theory of particle physics developed in order to mathematically model particle interactions with quantum mechanical equations, assuming axiomatically that the electron and proton have equal and opposite charges . So the answer to your

Why does an electron or proton posses the property of a charge?

Because they were discovered in the lab to do so , and the axiomatic assumption of their equal and opposite charge in the models describing atoms, molecules and nuclei has never been falsified by a huge number of data taking in the last decades.