Maybe a silly question but I am looking for an analytic explanation of it.
I think I already have one but I want to see if there is a better one, more fundamental?
What does it mean fundamentally although the proton to have a much larger mass than the electron but to have the same absolute charge value $e$? How is this possible?
Physics is not mathematics. We observe that the proton and electron have opposite charges of equal magnitude. We construct models that reproduce this observation and others. Thus, any "analytical explanation" from one of these models actually traces back to the observations.
You can't have reasoning from unquestionable axioms in physics. The universe gives us phenomena, not axioms.
This directly follows from the conservation of charge when considering the $\beta^-$ decay: \begin{equation} n\rightarrow p^++e^-+\overline\nu_\mathrm{e}, \end{equation} where the neutron $n$ and the electron antineutrino $\overline\nu_\mathrm{e}$ don't have charge.
