One of the basic differences between homeopathy and Western medicine is that it treats the whole person. This means that the case is taken, and a remedy is prescribed based on the unique combination of symptoms that that person has.
Western medicine is based around treating a disease. If you have X condition, then X medications are prescribed. If you have multiple diseases, then more and more medication or procedures are recommended. In this way the person and their problems are divided. Each person may contain a multitude of diseases, each with their own treatment and side effects.
Homeopathy treats the singular person, as a culmination of all of their symptoms.
Without a diagnosis, Western medicine is unable to treat your issue. Many people suffer from symptoms only to have all of their tests come back with no unusual results from the lab. What happens when you feel miserable, but a doctor is unable to tell you exactly what is wrong? Western medicine may only proceed if there is a diagnosis attached to your problem.
If test results are vague or misunderstood an incorrect diagnosis may be applied just to try to fix your problem. It is unsettling how often an incorrect diagnosis is given, due to lack of time to investigate the problem or due to conflicting or confusing symptoms which do not match an expected pattern. This rarely leads to a satisfactory resolution of the original problem. Worst case scenarios lead the patient from one incorrect diagnosis to another, all with treatments which do not relieve their pain.
Homeopathy does not require a diagnosis in order to treat the problem. Lab results and a doctor's diagnosis can be helpful, but are not essential when taking a case. Homeopathy is based on the symptoms that each person presents, in their own unique way. The symptoms as a whole paint a picture which can be matched to a remedy state. The remedy states cover combinations of mental and physical symptoms, so one can be found to best match your particular situation. Homeopathy is not limited by test results, or by mysterious symptoms that do not fall easily into a diagnosable category. The whole person is treated as the sum of their symptoms. In this way homeopathy can relieve suffering which defies easily diagnosed problems.