The Problem
Homeopathy is clearly nonsense. But of course people are free to do and think as they wish. Why then, is it a problem? Well, it leads to a number of issues.
Firstly and arguably most importantly is that public money is spent on homeopathy - the National Health Service spends larges amounts of money on it, they recently invested £10 million in refurbishing the Royal London Homeopathic Hospital installing features such has wooden floors because that is "better" for homeopathy. That money could have been spent on putting hundreds of extras nurses on the wards. But make your own mind up as to what would have been a better use of the NHS's money (or as a British tax payer, your money!).
Secondly, people may use homeopathic remedies rather than seeking real medical treatment. If someone tries to cure cancer with homeopathic remedies, which it clearly isn't going to do, they are simply delaying the time to which they see a real doctor and therefore reduce the time frame in which there is to catch the cancer before it becomes terminal. Homeopathic doctors are unlikely to diagnose real medical problems because the majority are not real doctors - there are no qualifications, training or licensing to practice homeopathy. Not that you really need any of that to hand out water but when people start putting their life in the hands of people claiming to be doctors, that then becomes a concern to our society as a whole.