Why Intermodulation products appear when two or more signals pass through a device whose output is not a straight-line function of its input. A nonlinear transfer characteristic contains squared, cubed and higher terms, and those terms mathematically generate sums and differences of the input frequencies, such as the troublesome third-order products at 2f1-f2 and 2f2-f1. A perfectly linear amplifier or mixer stage would simply scale both signals and produce no new frequencies, so intermod is always a symptom of nonlinearity, typically an overdriven front end, mixer or even a corroded metal joint.
Watch out Negative feedback is actually a common cure, since it linearizes an amplifier and lowers distortion; positive feedback and lack of neutralization lead to oscillation or instability, not mixing products.
No nonlinearity, no new frequencies. Mixing needs a bend in the curve.