Motivation behind the principle that all electrons are not distinguishable EDIT: It is usually claimed without providing much motivation that elementary particles of the same kind, e.g. electrons, are not distinguishable in principle: there is no way to distinguish between them. In particular this principle implies that any two electrons have exactly (!) the same rest mass and charge.
A similar question has been asked here Are all electrons identical?
The answer there is helpful, but I would be more interested to learn more on the motivation of this principle, probably more close to its historical development.
 A: EDIT: This answer was for the original question "Motivation behind the principle electrons are not identical." (IMO, the concept of distinguishability is more nuanced, I welcome reading others' answers on it.)

The guiding principle is that if you measure a particle that has different properties from an electron, you don't call it an electron. A good example is the muon, which has the same charge and spin as an electron, but greater mass.
Now, particle physicists will give you explanations for why we have the fundamental particles we do, so read into the Standard Model and further particle physics if you're interested. (I can't say anything further on the matter, because I'm not a particle physicist.)
A: Electrons are distinguishable, even though they have identical properties and identical quantum values (like half-integral spin), if you go with the meaning in statistics.
When you measure scattering experiments using fermions, the statistics match the theory for distinguishable particles, just as they do for two dice that look identical to us.  But when you look at scattering experiments with bosons, the statistics match the theory for indistinguishable particles.
Basically it's a question (again, with two dice) whether the outcome {2,4} is different from the outcome {4,2} .
