Why did Netflix split itself into two?

Basically self-protection. The streaming business is destined to become the de-facto method for pulling up movies and TV shows. The DVD-by-mail business (now called Qwikster) is destined to become a high-priced relic. Netflix is insulating the former from the latter. From Gizmodo:

There are two main benefits to cordoning off the mail service in the Qwikster ghetto. First, it keeps streaming customers shielded from the inevitable DVD price increases that will come with fewer subscribers and ever-increasing postal rates. And--maybe more importantly--Netflix is able to limit the constant reminders of all the movies that you can't add to your Instant queue. Streaming customers won't be able to see DVD availabilities any more, which means you won't get that feeling that you're staring at an unattainable ocean of truffles and bonbons with nothing but a Werther's Original in your hand.

There's also this point raised by Bill Gurley today: Netflix has this whole time been paying studios for streaming rights based on its total number of streaming subscribers, including those with streaming + DVD plans that never watched a movie online. By partitioning streaming and mail-order, Netflix can hand studios a more accurate picture of how many people are downloading their content--which will hopefully mean more favorable studio deals, and more options for your queue.