My personal view is that cables usually do make difference (and I did not know headphone cables can be questioned, as usually, the most aggressive discussions are about power and digital cables) but whether a person is able to hear it depends on various factors: level of audio gear, specifics of the audio tract, the ability of a person to hear minor details (it requires a lot of training), mood, weather, etc..
I find it quite honest that you mention "mood" in the factors you recognise as playing a role (and even the weather, I was not expecting that one...) .
If you look at a train track or at a road, from a perspective not perpendicular to them, your visual system will make you see that the rails or the sides of the road are not parallel, but intersect at the horizon. Your experience is real.
Now if you move to different positions, or follow the train track or the road, you will realize that in reality both rails or both sides of the road are actually parallel and not intersecting.
So your vision system can easily be fooled, but additional approaches can help in realizing this and discard authentic but illusory perceptions.
These examples are easy to verify and universally accepted.
The human auditory system is certainly not better than the human visual system (actually much more error-prone). It may make you really perceive clear differences when hearing through different cables. Most people here are not contesting that you do hear differences between cables.
What people want to convey is that these authentic experiences are illusory, just as the train rails intersecting instead of being parallel, and that you may just as well have authentic experiences of hearing differences with the very same cable: it's all happening in the brain, but only in the brain, there are no differences in the outer world.
Measurements such as those shown by Amir should call for a cautious evaluation of what one experiences with his auditory system, for critical thinking. Please look first at the measurements and take some time to think about it and let it sink and settle down.
Another thing which should make one suspicious is that there are companies and fake reviewers paid by these companies (directly or through ads or through giving expensive items for free which can be sold for a lot of money) that play on this subjective feelings to make a lot of money by deluding people into purchasing very overpriced products which are objectively bad or useless or not making any difference in the real world outside one's brain's illusory feelings.
Have a nice weekend,
bidn