HCG fails because it is backed by bad science. Homeopathy fails because it is fundamentally anti-scientific. Homeopathy rejects science and the scientific method and embraces (selectively and conveniently of course) the belief that effects need not have causes and that nothing is something. If that sounds crazy, well it is.

Another Crackpot Theory of the Nineteenth Century:

Much like today, 1800s were an era of great progress and incredible stupidity. The germ theory of disease, public sanitation and the emergence of modern medicine are examples of some of the great, staggering achievements of that era. Homeopathy is an example of the stupidity.