It doesn't.
Homoeopathy has no plausible mechanism to work, it's never been demonstrated to work in high quality trials and there is no rational reason why it should work either.
Homoeopathy is based on two concepts "like cures like" (e.g. if you are having problems sleeping, give something known to cause insomnia as a cure) and the Law of Similars/Law of Infintesimals meaning the more a substance is diluted the more powerful it becomes There is no evidence to support either of these laws. Science tells us that dilution of a substance to such an extent that barely a single molecule of any active substance remains, leads to the original substance being absent from the final preparation.
Homeopaths claim that water has memory..this theory has never been proven. This idea is akin to throwing a pint of beer into the sea and drinking the sea water hoping to get drunk. The "water has memory" concept is the most ridiculous out of all the homeopathic principles. Even IF water had memory, homeopathy would still be implausible. Homoeoquacks claim that they can control exactly what the water remembers...So basically they claim to be able to do something scientifically impossible, with something that does not exist in the first place!
Homoeopathy is supported by a long line of fallacious arguments, -including conspiracy theories, methodologically inept trials, personal anecdotes and quantum BS. If they get nowhere with that, they invent ad hoc meta-analyses and hope that no one has the sense to see what they’ve done. It’s bunk.
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And just take a look at the logic (or lack of as the case does) in Omoikane's answer!
Check out the special pleading fallacy. Notice how he does not even attempt to present data to support homeopathy, instead he claims he won't because we won't accept it! So what he's essentially saying is that we are wrong simply because we won't accept poor evidence! Science does not give credence to this type of childish uneducated BS. This is a sure sign of a crank, if there is robust evidence that demonstrates homeopathy to work, we'd be forced to change our position.
Look lets cut the BS, Mr E and the like simply don't supply evidence because they can't- there is none. Mr E has provided ridiculous links in the past, and we'd refuted them. Now he's too embarrased to submit anything and has resorted to using fallacious arguments as a reason for there being no data demonstrating homeopathy- this is pure insanity!
Whats chiropractic got to do with this question Mr E/Omoikame? How about you answer the actual question which is about homoeopathy instead of using red herring fallacies. However, since you brought it up, just because chiropractic has been around for over a century does not demonstrate efficacy. This is a logical fallacy.
It's STILL a LOL FAIL guys but thanks for the laugh.