"Physician" is regarded as the highest position in medicine, thus their words carry significant weight, and will be taken as the truth in most cases. His patients will start to believe that homeopathic remedies are valid medical treatments. A few of them will get better, either because of the placebo effect or the body's natural tendency to self-heal. Regardless, word will begin to spread that the homeopathic remedies has cured some ailments and other people will also start to believe that homeopathic remedies are scientifically proven treatments. This can pose a threat to public health safety.
One role of a physician is to guide patients towards decisions that reflect their best interests. They must thoroughly educate patients on treatment options (even homeopathic ones) and dispel misinformation. In the case of homeopathic treatments, it's important to have a discussion as to why they could potentially be dangerous and the validity of their therapeutic effects (or lack thereof). Engaging in white lies and deceiving patients violates the inherent trust that patients place upon physicians, and it can lead to severe ramifications. However if the patient is adamant about receiving homeopathic treatments, even after being thoroughly educated on the matter, you have to respect the patient's autonomy and wishes.