his contemporary peers in the idea that all individuals have a good and a bad side, and that each is independent from one another.

Let's briefly mention that the duality of men was a hot topic throughout the entire 19th century. Dr. Jekyll and Mr. Hyde was published in 1886, which is 68 years after Mary Shelley published Frankenstein, and 15 after Charles Darwin published the fascinating The Descent of Man. All three of these publications are intertwined by the essential questions: a) Who are we, really?  b) What are we supposed to be?,  c) Are we supposed to be "this or that"? and, d) What is our life meant to be?

As a result of the social changes, Victorian literature often attempted to go in depth with the study of human behavior. A lot of paradigms and constructs had been shaken from their foundation. The influence of the Industrial Revolution, Darwin, Freud, the economy, science, and medicine, all together, caused the 19th century to literally see the world change, in a manner similar to how our modern society witnessed the world changing after the advent of the Internet. 

All this being said, at the time of Jekyll and Hyde, psychology was budding into a social science, and many ideas regarding human personality rocked the former idea that humans were entirely static, rather than dynamic.

When Jekyll ascertains that all individuals have the same capacity to be good and evil, at will, he is also saying that within each of us there is a battle between an "angel and a fiend".

The problem is that Dr. Jekyll's hypothesis is deeply flawed and does not match the statement that we are analyzing. His idea was to get a potion that would split the "angel" and the "fiend" that inhabits the individual so that they each act individually. The potion would take the fiend (Hyde) out of the "angel" (Dr. Jekyll) and each would be their own person. However, we know that Hyde had more power, and that eventually evil was gaining territory. Jekyll ended up creating a bad version of both.

Dr. Jekyll find this out through his experience with being both himself and Mr. Hyde.  What he finds out is that there really are two sides to him.  He is saying that he (and all people as far as he can tell so far) is made up of two sides.  There is a good side and a bad side to everyone.

The only reason that Jekyll is not sure about this is that he think that there may be even more sides to people that other people will discover.  But he says his own work shows that there are at least two people in each of us.