(I highly recommend Professor George Vithoulkas' book The Science of Homeopathy for an in-depth discussion on this topic and how homeopathy works).
There are many answers to this question. Homeopathy has suffered greatly in the last few years due to the concerted efforts of the medical establishment and the mainstream media to undermine it. It is clear that many of these people know very little about homeopathy. Other than the placebo effect argument (discussed in the previous question) and the ensuing call for certain government funding for homeopathy to be discontinued, the other main argument is that Homeopathy is unscientific.
Science can not explain everything. Like all other disciplines, It is a human discipline and endeavour that seeks to find out and make sense of the universe around us. It is a tool of discovery. To discover something is to realise a fact that was already true before it was discovered. Science did not make it true. The fact that something works but as humans we do not entirely know how is not a reason to dismiss the actual fact. Rather we should accept the fact whilst acknowledging that we have not yet discovered the how and why.
Recent developments in various branches of science are already telling us that homeopathy is much more scientific than it has been made out to be. Developments in new-physics, research into the properties of water, and ...