A strong distrust of the medical establishment is why pointing out simple facts like "homeopathy has never been shown to work" may be insufficient to get a homepathy user to use medicine instead. There's motivated cognition going on – if you don't think medicine works, what are you gonna do when it turns out your alternative doesn't work either?! Just conclude there exists no substance that will help any health problem, and let God sort you out?
Basically if you care about a homeopathy user and want them to use medicine, it isn't a productive approach to say homeopathy doesn't work, because even if you convince them it doesn't work, they will still decline to use medicine because they feel they can't trust it.
This distrust is built on experience that hospitals seek to make money to the extent of only ever caring to treat superficial symptoms, and are actively interested in keeping people sick. Well—hopefully it's built on experience. It could be built on a huge pile of anecdotes that the user bought into because it fit into e.g. an anti-corporate world-view. This is one reason it's so important to understand that anecdotes are not experience or evidence, even if they feel similar!
This same reasoning also seems to fuel the Anti-vax group and probably others, and ultimately the poor souls in the overlap of all these groups seem to be trying to reinvent medicine from scratch with new-old interpretation frameworks like "Detox", which ret-cons all development in medicine since Hippocrates, pretending it didn't happen so you can re-do the research, how fun! That's easy to do when you don't know the history, which is why people should study history!
Question: why would the same logic behind distrusting the medical establishment not apply to their homeopathic doctor? Homeopathy is big business, just like health care, so are they any different wrt. profit motive? One difference is that health care is partly government-regulated, but that doesn't necessarily say anything since so many governments are corrupt.