Actually, they're not.
Homeopathy is actually capable of helping a bit with minor headaches, in a way. You know how? The medicines are usually diluted in water
. And you know what is the most common cause of headaches? Mild dehydration
. Which can be cured by, you guessed it, drinking water. Of course, a cheaper variant of this therapy is to just drink non-homeopathic water, but you couldn't say the more expensive one doesn't work, either.
Of course, this doesn't change the fact that the supposed "active ingredient" doesn't do anything (and may not even be there), but the therapy as a whole has a good chance of helping with that particular kind of headache. Given who tends to buy into things like homeopathy, I wouldn't be surprised if all
reported cases of homeopathy actually doing anything were things that could be helped by just giving the person water.
This is actually a good example of why interpreting clinical trial results is not straightforward. Say, the results in homeopathic therapy group and in the supposed "placebo" are exactly the same, but some people did
get better. You can dismiss it right there, without explanation, or you can dig deeper and find that you've given both
groups the real remedy (this being the plain ol' water). You could then (money permitting) run the same trial, but this time specifically for people for whom you can be sure that their problems won't be solved by drinking a glass of water (while telling everyone else to help themselves to the water cooler). Then
you may get a meaningful result.
And yes, I imagine some quack chiropractics did actually stumble on something that'd help with a back ache. Pity that they're only interested in big name cures. When someone is trying to get rid of cancer, a back ache suddenly getting better could be disregarded. And besides, they'd probably go "Extra deal! It cures cancer AND back aches as a bonus!" even if they could reliably repeat that (not every back ache is the same, after all). I don't think any of those quacks ever thought "Well, it doesn't seem to help with cancer, but it's the third patient who had his back stop hurting just before croaking... maybe I should change my sales pitch?".