Why are we using positive feedback for low-pass and high-pass filter?
Coming back to the original question: WHY...?
The answer is as follows:
*Passive RC filters allow negative-real poles only (very bad selection properties)
*Thus we are using either passive RLC filters, which enable conjugate-complex pole pairs by exploiting the resonance effect (and improved selection properties), or
*We use active RC filters, which also cause conjugate complex poles if
positive signal feedback is applied (typical example: Sallen-Key structures, however with negative dc feedback)
Comment: However, all other active filter topologies also apply positive signal feedback and negative dc feedback (MFB, Integrator filter,...) insofar as the signal feedback network causes a corresponding phase shift, which in conjunction with the inverting input terminal of the opamp acts as positive feedback.
In summary: To construct active RC filters with good selectivity (Butterworth, Chebyshev,...) we need complex pole pairs, which can be realized with positive signal feedback only (in addition, a stable bias point requires negative dc feedback) .
Supplement: To complete the picture it should be added that there are also "negative-gain Sallen-Key structures" (with much larger negative fixed gain values than the classical pos. gain S+K topologies). However, here the same applies: The feedback network (connected to the inv. input terminal) introduces phase excursions, which turn the negative into a positive signal feedback.
This is a good example to verify that "positive feedback"
not necessarily means: Feedback network is connected to the non-inv. input terminal.
In turn, there are cases where negative feedback is connected to the non-inv. terminal (if phase inversion takes place within the feedback path). Example: Actively phase-compensated opamp circuits.