This assumption is made out of the author's fancy.
He visibly does not have a clue about quantum physics and how fundamentally different it is from classical mechanics.
Quantum physics defines the electron as a fundamental particle. Thus it has no "internal structure" except for the cloudiness of its presence which, when measured below some resolution, mixes with the virtual electron/positon pairs of the quantum void fluctuations so that it can no more be distinguished from these fluctuations.
So this is quite a complex story, however the idea is that electrons have no parts of
any nature different from themselves: cutting it in 2 probably gives back one electron on one side and possibly one or more electron/positon pairs on the other.
In particular, the spin is a fundamental quantity in quantum theory, and the one of the electron is rigorously indivisible.