You have decided on your main points, the material in the bull's eye that will lead you to the response you want. Now you need to gain understanding of and agreement for each point. It clarifies, illustrates, makes memorable. Anecdotes, statistics, testimony, explanations and repetition are used as supporting points. Visual aids can also be thought of as supporting material because they make your main points more vivid.
Anecdotes are fun.
They add interest to your speech. People remember them. They support and clarify an issue, but shouldn't be expected to prove your main points by themselves. Anecdotes have been used by great teachers since time immemorial. Aesop's fables are all tales told to illustrate moral lessons.