Why is electric charge conserved?

Question

We have long been taught that electric charges are neither created nor destroyed. But somehow it is okay to destroy two oppositely charged particles at once ! Why is that so?

Let's just take a look at electron-positron annihilation; Two equally oppositely charged particle are bombarded into each other, both are instantly destroyed (lose their existence) and gamma ray photons emerge. It is certainly convenient to say that at $t$ second the net charge in system was 0 and at $t+1$ second it is also zero. But certainly it also raises the question what if you observe only a positron or an electron, in observed system certainly charge will not be conserved however overall it maybe.

It jumps out and say that you cannot destroy individual charges, but if you get 2 equally and oppositely charged particles we can destroy both ! (kind of Romeo-Juliet) Then why is the fundamental postulate of conservation of charge that /charge can neither be created nor destroyed"? Since, clearly it can be destroyed, just in pairs (also created in pairs)

Answer 1

When opposite charges annihilate, all conservation laws must be obeyed. 1 + -1 = 0, before and after for charge. If it is an electron squeezing into a proton to make a neutron, an electron neutrino is emitted and all conservation laws are obeyed. Following are symmetries and their associated conserved quantities via Noether's theorems. The universe does not cheat (except for discrete symmetries. Noether can leak through a loophole).

Invariance                  Conserved Quantity 

Proper orthochronous Lorentz symmetries 

translation in time (homogeneity)   energy
translation in space(homogeneity)   linear momentum
rotation in space   (isotropy)      angular momentum

Discrete symmetry 

P, coordinates' inversion   spatial parity
C, charge conjugation       charge parity
T, time reversal            time parity
CPT                         product of parities (100% conserved)

Internal symmetries (independent of spacetime coordinates)

U(1) gauge transformation   electric charge
U(1) gauge transformation   lepton generation number
U(1) gauge transformation   hypercharge
U(1)Y gauge transformation  weak hypercharge
U(2) [or U(1)xSU(2)]        electroweak force
SU(2) gauge transformation  isospin
SU(2)L gauge transformation weak isospin
PxSU(2)                     G-parity
SU(3) "winding number"      baryon number
SU(3) gauge transformation  quark color
SU(3) (approximate)         quark flavor
S((U2)xU(3))
[or U(1)xSU(2)xSU(3)]       Standard Model

Answer 2

We have long been taught that electric charges are neither created nor destroyed.

No, we have not been taught that. We've been taught that electric charge, i.e., the net electric charge, is conserved.

Imagine that, within some volume there is some net electric charge Q. Assuming there is no current through the boundary of the volume, we are taught that the net electric charge within the volume will always be Q. This comes from the continuity equation

$$\frac{\partial \rho}{\partial t} + \nabla \cdot \vec J = 0 $$

which express the conservation of electric charge.

Now, the fact that Q does not change with time does not imply that pairs of oppositely charged particles cannot be created or destroyed.

For example, assume $Q = 0$. This means that the number of positively charged particles must equal the number of negatively charge particles at all times. But this does not mean that the number of charged particles within the volume must be constant.