Academic vs Intuitive Plausibility

When I hear about something like homoeopathy, once I learn of what it is I can't see any way in which it could work. There's just no scientific plausibility to such a notion at all. Yet intuitively there's always the question of "what if?" And no matter how much I can read on homoeopathy and see it academically as nonsense, I have the intuitive notion not to dismiss it. If homoeopathy could work it would be great, to be able to take a pill that would cure cancer.

I can understand why negative positions don't sit well with people, and why it would seem dogmatic to reject the possibility of something. But being open-minded cannot simply be accepting any old claim, because claims on their own feel more plausible than may be warranted by the evidence.

That same intuitive plausibility is why I still take vitamin C tablets when I have a cold, even though I understand academically that there's no real effect. After all, it might work.