Last TM one of the newer members advocated homeopathy as her #3 speech. I had to do the evaluation - but I managed to stick to the mechanics of the speech (which is what TM is actually for) when I really wanted to rip into the subject matter.
She pointed up the early research into quinine (and sort-of implied that homeopathy discovered that treatment for malaria), pointed to positive results in animals (so where is the placebo effect then?), and finally asked "where's the harm?"
I actually didn't know about the quinine one - turns out the researcher (Dr Sam Hahneman - the founder) mistook an allergic reaction (quinine allergy is pretty rare but it seems he had it) for the normal action of the substance on a healthy body. So bang goes that one.
The placebo effect in animals is well documented. Same with babies. No homeopathic remedy has ever worked better than placebo in double-blind trials with any group; animals, babies, whatever. The thing about scientific medicine is that it does it's thing whether you believe in it or not.
And the harm - apart from Hahneman's historical support (from homeopathic principles) for an erroneous idea about how cholera is spread killing many who may otherwise have been saved, there are many many documented cases of people who have been harmed or killed for failing to think critically about homeopathy. Usually the harm is due to discontinuing real medicine in favor of this snakeoil. Sometimes it is due to economics - do you buy the medicine or the homeopathic remedy?
If the remedies had the effects homeopaths claim for them, they would be restricted, prescription only, drugs.
In the UK, homeopathy is publically funded as a "complimentary" medicine ... and it is favored by physicians precisely because it does not do anything. There is research that shows complimentary treatments improve recovery times once the real medicine has taken effect.