As we've just read, there is undoubtedly a bunch of reasons to stop coding when you become a manager. However, there is also a bunch of reasons, with some being contrarian and counter to those to stop coding, to keep coding!
Some of these reasons are alternative views altogether. Since neither software development nor management are binary concepts with definitive rights and wrongs, both effective software development and management require the ability to work with ambiguity and, sometimes, conflicting points of views.
It's a balance between science and art, dealing with pure logic and real people. In short, there are no absolutes.
From a personal perspective, one of the main reasons to keep coding is simply to stay relevant. After all, you are still working in the business of software development. Knowing about the latest technologies, techniques...