Why Unwanted oscillation happens when enough output energy feeds back in phase to the input, usually through the device's internal capacitance (plate-to-grid or drain-to-gate) or through stray lead inductance that resonates at VHF. Neutralization cancels that internal feedback by deliberately coupling a small out-of-phase sample of the output back to the input. Parasitic suppressors, typically a few turns of wire in parallel with a small resistor placed in the plate or drain lead, add loss at VHF where the parasitic resonance occurs while barely affecting the operating frequency.
Watch out Tuning both input and output for maximum power is a normal amplifier adjustment for efficiency and output, but it does nothing about feedback paths and can actually make an unstable stage break into oscillation.
Instability = feedback. Kill it two ways: neutralize the internal capacitance, suppress the VHF parasitic.