Here's a post by Jose Valim on the reasoning behind the change:
As a quick summary, Capybara is an acceptance test framework and as such, tests should be written from a browser or user's perspective. With the rspec-rails gem, tests found in spec/requests directory have access to methods that expose lower-level details like requests and responses(methods like get, put, post.) So if Capybara tests are also found in that same spec/requests directory, you are able to use both the Capybara DSL and the free methods that are meant for integration tests which causes a conflict and leads to some developers using a mix of both. This leads to ugly test suites.
The solution they came up with is to create a separate directory meant for use with Capybara DSL, which is spec/features and another directory (spec/api) meant for use with the Rails provided integration test tools.
Michael Hartl will be releasing a newer version of his tutorial sometime in the future which will provide more up-to-date material. You might also want to look at RSpec's 'expect' syntax for its assertions. They plan on deprecating the 'should' syntax possibly as early as RSpec 3.0.