How does armature reaction affect brushes in DC generators?
I'm not familiar with the theory of DC generators, but what your sources are trying to explain sounds fairly straightforward just on general electrical principles.

Look at the brush/commutator connection as a switch. In any kind of switch, when contact is made or broken, there will be a short time period of very high resistance (whether this involves arcs or merely a small contact area). That resistance will dissipate power uselessly, and arcing will cause wear.

If you instead arrange the timing of the commutator so that the contact is only made or broken when there is no potential difference and therefore no current — or, realistically, just very little — and the majority of the current flows while the commutator is “fully on” (contact over the entire area of the brush) then there will be no/little dissipation or arcing, so the generator will be more efficient.

That point would be when the magnetic field and armature are aligned so the magnetic field does not induce any voltage (the “neutral plane”) — the same position as when, if it were an AC generator without a commutator, the output voltage would cross zero.