The first task you will need to do in writing such a persuasive essay is research to discover what sort of alternative cancer cures are considered as having some basis in scientific evidence and which are simply scams or wishful thinking. This analysis will also include making sure to sort reliable from unreliable sources and select articles from peer-reviewed journals.
The first site you will want to visit is the Food and Drug Administration one, which has several excellent articles on how to tell if a health product is a scam.
Another concept you might want to clarify in your speech is the difference between alternative and complementary therapy. The term alternative therapy means forgoing all forms of regular cancer treatment in favor of such things as faith healing, "cancer" diets, magnetism, and other modalities, and not enduring such proven but highly unpleasant medical treatments such as surgery, radiation therapy, and chemotherapy. A discussion of the difference between the two and a list of resources which can help you find reliable sources on complementary and alternative therapies can be found at:
Your next major decision is whether you want to focus your speech on alternative or complementary therapies. For the latter, your main line of argument will be much easier. You can state that most forms of cancer treatment are painful, stressful, and generally unpleasant. Many alternative therapies such as massage, acupuncture, and meditation have been proven to make patients undergoing cancer therapy feel better. Even if they do not contribute directly to survival time, anything that helps manage pain and stress is obviously a good idea. For such a speech, you could site many studies on the positive psychological effects of such complementary therapies.
Arguing for alternative therapies is somewhat more difficult. You probably don't want to talk people out of procedures that could save their lives, such as surgery to remove early stage breast cancer. What you might do is focus your speech on a particular group of patients, such as those with terminal cancers, and argue that for this population, alternative therapies or hospice care provide better end of life quality than traditional hospital based care. A good discussion of reputable evidence supporting this position can be found at:
Here you should start your paper out with an argument that if a patient has advanced stage cancer, and there is no possibility of a cure or even a significant period of remission, then rather than subject the patient to painful procedures and medications with unpleasant side-effects in a hospital setting, alternative medicine may offer better quality of life.
I need a persuasive speech. I would like to share a speech with my audience that has a powerful message.