> If the user can't remember where they came from, why would they want to go back?
Because "back" is often conflated with "out"--the user might simply be done with the task and wants to get out. Unfortunately, the app simply shoots them to the previous app on the stack, which may or may not be where they want to go or remembered they came from.
Ex: Many apps go to the browser, but the user might not remember which app sent them to the browser. They might have thought it was Twitter, when it was in fact the home screen.
To enlighten you, the home double tap in iOS does not take you straight to the previous application. It brings up iOS's multitask tray that has the four previously viewed apps on it, in order of recent use. The first app on it is always the previous app. You can see which one it is. Android doesn't show this to you, nor do you even have the option of getting to the previous app unless you are at the bottom of the stack.
Edit: We're arguing about the merits of having a dedicated back button. If an advantage to the iOS task switching feature is found in yet another button on Android, that doesn't contribute support to the back button's existence.