True, true, you are right. It is quite the connundrum though... It is extremely trivial, and yet it seems very difficult for people to drop the notion that a PHASOR phase equates to a time delay, which is does not.This is an cases of estimation bias.
If you search for Creationism vs. Evolution. you will also get the impression there is a controversy.
Don't think you can educate them or that they want to be educated.
If they would have the knowledge/educate to understand your explanation they would not argue.
- A polarity switch equates to a sign inversion.
- When all we have to characterize a signal or system completely are magnitude and phase phasors per frequency, the sign change has to go into the phase somehow, as the magnitude is unaffected by the sign.
- Whether looking at truncated sines, triangular, or whatever other signals, all of the Fourier components that make up these signals will have their phasor phase shifted by 180 degree when going through a system that flips polarity, and the output signal will be the "upside-down" version of the original signal.
- There is no delay associated with this flat phase characteristics (why would there be?)
- You cannot time delay your way to a polarity (so why try).