When I say that homoeopathy is magic I do not mean it as a metaphor or analogy, I mean that its principles are a variation of those of sympathetic magic.  The term sympathetic magic was first, as far as I know, coined by Sir James George Frazer in The Golden Bough. He wrote:

If we analyse the principles of thought on which magic is based, they will probably be found to resolve themselves into two: first, that like produces like, or that an effect resembles its cause; and, second, that things which have once been in contact with each other continue to act on each other at a distance after the physical contact has been severed.

In fact he goes on to call the former of these principles “homoeopathic magic”.

This is the basis for many traditional systems of magic around the world. For example, two widespread ways of cursing someone are to use images or dolls of them (the first principle) or to use their hair or toenail clippings (the second principle).

Now consider how a homoeopathic medication is typically made:

1. A substance is chosen which produces similar symptoms to the sickness to be treated.
2. It is repeatedly diluted with water, each time taking just a small amount from the previous dilution, until it is unlikely that even one molecule of the substance remains in the water.
3. This water is then used in the manufacture of pills: but is evaporated in away in the process.

The first step in the process relies on a modification of the first principle of sympathetic magic: that like cures like, rather than affects like. Of course, it relies on similarity of symptoms, rather than similarity of appearance. It does not depend on the cause of the symptoms, but on similarity of visible, or otherwise easily perceptible, symptoms.

The remaining steps rely on a variation of the second principle. Rather than the water acting on the substance it has been in contact with, it retains some property it gains from the contact. Similarly, the pills retain that property from the contact with the water.

While homoeopathy is an interesting variation on the principles of sympathetic magic, I cannot see how it can be denied that it is a variation on those principles, rather than something entirely different.