Homeopathy is a pseudoscience. The core tenet of homeopathy is “that which causes a symptom will also cure it.” This of course is very false, but it stuck around because there are a small number of cases where by complete coincidence an effective treatment for a disease happens to cause symptoms similar to the disease when administered to a healthy person.
Homeopathy is a pseudoscience because when put under test and the test indicates that there is no result, homeopathic practitioners don’t question the premise that led to the treatment, but rather come up with anything and everything else that could be wrong. One of the core tenets of science is that when a hypothesis is disproven, it must be discarded, and experiments should seek to disprove hypotheses rather than confirm them.
Allopathy is a derogatory term thrown at non-homeopathic practitioners by homeopaths. It essentially translates to “the cure is something other than the cause.”
There’s lots about “allopathic medicine” that works. And when they find something that indicates something doesn’t work, eventually the practice stops. They’re also free to challenge core tenets as they please, rather than being forced to try to fit everything to “that which makes sick also cures.” For instance, the old hypothesis that ulcers are caused by stress had been ingrained in doctors’ heads for decades, until one doctor finally managed to persuade others that it’s caused by a particular bacterial infection by infecting himself and getting ulcers. I’m hoping to see a lot more of that on other medical problems, including chronic fatigue syndrome, depression, irritable bowel syndrome, and other major issues with default treatments that often either don’t do anything or eventually go away on their own over the same timeframe that the treatment is “supposed” to work.
One of the claims of homeopaths is that “allopaths” don’t treat the whole patient or that they just fight symptoms. While with many doctors this may be true, it isn’t anywhere near universally the case. They’re harder to find, but you can find doctors who will work with you and seek to understand your real problem rather than just cherry pick a few of the symptoms and call it whatever thing comes close to a textbook definition.