The purpose of a headphone cable is to transmit a signal from one location to another. High-end replacement cables claim to be able to transmit that signal "better".
Has anyone done objective testing on these cable claims? Take two cables, connect them via a splitter to a source. Connect the ends of the cables to a Wheatstone bridge circuit. Place an oscilloscope lead between the two leads so you're measuring the time-dependent voltage difference at the ends of the cables. Play some music and see what the actual difference is?
Sure, there's lots of design and testing with some cables. Mostly high power lines and cables for very high frequencies and antennas.
With those, test results do show measurable differences to exist and they also behave according to known science.
Curiously, audio cables - if the believers are to be believed - do not behave under any known principle of science. They cannot be measured. Test equipment, some of which is used to develop other cables, becomes ineffective and/or unreliable. Further, anyone who tries to apply similar methods is "hateful" and trying to suppress knowledge and truth.
Another way to look at this is assuming that every believer's claim is accurate. Never mind that the claims conflict most of the time. But if even a fraction of the claims were true, it would mean that many electrical goods we have should not work as they do.
Audio gets put on some special plane of purity. It isn't. There are thousands of applications with far more critical tolerances and performance issues. My amateur radio is like that. It's a complex unit with DSP, transmitting section, and lots else. Now, if tiny bits of metal in a wire, power cords, etc., made a difference, then those differences would probably screw up delicate functions inside. Same goes for all sorts of other electronics.
I'll put that argument yet another way. If it were shown or demonstrated that cryo'ed silver strands wrapped in fine silk and bathed in the tears of a virgin Tibetan monk improved, say, antenna reception in aircraft, then, believe me, the patent lawyers would be dispatched and there would be freakish amounts of work at the USPTO detailing this. If something has audio applications, it also has commercial and industrial uses. Electricity doesn't know the difference between some precious NOS tube and a commercial food dryer. If different cables made improvements, then industry would be all over it.
Another curious thing is the difference in cable costs. Most cables are priced fairly. Cover costs and make a fair return. However, the cables that claim science is wrong and that people who ask questions are full of "hate" are priced, typically, several hundred percent over costs. In fact, you'll often find $20 or $30 of materials being sold for several hundred.
Ask them why and hear yourself called a hateful, close-minded zealot with an agenda.
Maybe they're right. Or maybe they have something to hide.