A challenge when debating homeopathy practitioners is that they simply don't understand how the science industry works, they don't realize that if there were a shred of possibility that homeopathy made any sense there would be an ARMY of scientists all over it, elbowing each other aside for the fame and the glory ... and the probable Nobel. The whole homeopathy thing exists in an utterly different universe and therefore no Nobel is available. The quoting by homeopaths of a study here or there as evidence that homeopathy works would be simply laughable if it wasn't used as justification for a whole industry created out of magic cloth. You can't make something real by using stray threads that aren't repeated by further studies; stray threads are insufficient to make a whole cloth.
It all makes me think of the Philip Pullman series His Dark Materials. In these novels you learn that there are parallel universes where the laws of physics, chemistry, biology behave differently and magic is real. The first book exists in one of those parallel universes. Later in the series you learn that our world does indeed exist within the story and that with a special knife--the Subtle Knite--you can cut the barrier between the worlds and slip from one to another. Perhaps homeopathy does work but in some different world, and all the true believers are escapees from that world, unable to comprehend this world and the realities of science here.