Why? How does someone saying homeopathy works affect you? Is there a concern that you might believe it?
Empathy is a thing; we can care about an unfortunate outcome even if it doesn't affect us directly.
When someone, say, dies of preventable cancer because they were duped into believing that sugar pills were real treatment, this is a tragedy... even if I didn't know the person myself.
The mind controls the body. The placebo effect is a thing. If homeopathy worked for that person, it's possible it can work for someone else. Does your challenge help the person that it might have worked for?
You're overstating the placebo effect. I don't blame you, because that (mis)interpretation gets used a lot.
The placebo effect is almost entirely about these issues:
- selection bias: the type of people who would want to participate in (or would be eligible for) a medical study are often not perfectly reflective of the overall population.
- experimenter interference: the team running a trial may try to push for a favourable result, either consciously or unconsciously. If the study is properly blinded, then this push will affect the control group as well as the treatment group.
- a "helpfulness" bias: many people like to help others or feel pressure to meet exprctations. In clinical trials, this can mean the participants will try to provide the result that they think is expected of them (e.g. report lower pain levels after a treatment).
- effects of the trial itself: when someone goes to a clinic twice and week and gets peppered with health-related questions, this can put their health front-of-mind and prompt them to make lifestyle changes (e.g. improving their diet).
- statistical noise: every sample will vary from the true mean a bit.
Citing the placebo effect as evidence of the "healing power of the mind" is, IMO, dishonest... though I certainly don't think that dishonesty originates from you.