You need to use an API because your app is going to act as the user, and you are not going to rely on an external browser remembering the user's login. This is more convenient for the user, and, as well, mobile users are more likely to be using a native Facebook app, and wouldn't normally be using the browser to access Facebook.
oAuth and the API allow your app to act on behalf of the user, without the user giving your app their login credentials.