Your question, "What is the origin of the Continental vs. Analytic divide?" will probably not return many satisfying answers. There is no precise origin because the topic is very complicated and not well defined. The terms "continental" and "analytic" are not even clearly applicable to the differences today because of the global prominence of analytic philosophy approaches, and the increasing treatment of "continental" approaches by prominent "analytic" philosophers.
There are, however, several approaches one could take to answering the question. Here are the most prominent approaches:
The first is historical. DBK's recommendation of "The Parting of the Ways" is good, but, in my opinion, it could leave readers with the mistaken impression that "continental" philosophy derives its philosophical positions from Heidegger's ostensible politics. Ostensible because there has been a lot of ink spilled on what to make of Heidegger's membership in the National Socialists (i.e. Nazis) and the strange series of events surrounding the departure of his mentor Husserl from Freiburg in 1928 and Heidegger's eventual acceptance of the rectorship in 1933. Historically speaking, a large fraction of what is today considered "continental" philosophy derives from Phenomenology, e.g. from thinkers like Brentano, Husserl, Merleau-Ponty, Sartre, Derrida, among others.
The next approach is stylistic. The principal complaint that is leveled against or attribute that is used to describe Continental is that its "style" is characterized by dense, opaque, verbose language filled with word-play contortions, and inconsistent application of clean logical argumentation. In contrast, analytic proponents will often emphasize the importance of distilling philosophical disputes into formal logical representation, and will also argue that continental philosophy would be improved if it could just clean up its language, noting that analytic treatments of continental topics are often better. Brian Leiter is strong proponent of this kind of answer.
The next approach is philosophical/technical. Technical differences are too complex to get into in this forum, but for a good introduction to "continental" philosophical assumptions and approaches see Simon Critchley's book Continental Philosophy: A Very Short Introduction and Hans-Johann Glock's book What is Analytic Philosophy for a good overview of what is "analytic" philosophy today, or Dummett's Origins of Analytic Philosophy for a more technical treatment.