Why do linear time varying system exhibit frequency conversion
Any nonlinear transfer function will produce intermodulation a certain amount of sum and difference frequencies of two different input frequencies.
A single frequency will produce harmonics according to the order of power in the nonlinearity.
e.g.

BJT and FET current gains produce 2nd harmonics from quadratic effects (Ic vs Vbe).
Square waves are caused by nonlinear limiting and if perfectly symmetrical produce only odd-order harmonics.

This non-linearity also includes time-varying gm or hFE in the transfer function.  e.g. Gilbert Cell multiplier, balanced-diode modulator

for more examples, consult Wiki.

https://en.wikipedia.org/wiki/Distortion#Harmonic_distortion
https://en.wikipedia.org/wiki/Second-order_intercept_point
https://en.wikipedia.org/wiki/Intermodulation