These are the anti-patterns I see in your proposed approach:
Subverting user intention: The user indicates they want to do one thing (exit the app) and you substitute a different task (asking for feedback).
Highly interruptive: A likely reason a user would be quitting an app is because they really need to do something else right now. Interfering with this degrades the UX of the whole device. ("I need to quit this app to take a picture! But the app won't let me out! Now the world will never see the majestic yeti")
...of a highly standardized task: You're talking about overriding the operating system UI and even the hardware interface here. That's not something to be taken lightly. Exiting an app is something that should work consistently across all applications; your app breaking that contract will be disorienting to the user.
Garden pathing: The "exit" button brings up a page with two links: give feedback (not what the user planned) or "return to my stuff" (the opposite of what the user planned). The user has to read the fine print to figure out that to do what they planned -- leave -- they have to hit the exit button twice. You are really pushing the user away from their intention and towards that feedback form, to the point of obnoxiousness. (Seriously: that's skillful design work, I'm impressed, but you're very much playing for the dark patterns team here.)
The wrong question anyway: You're trying to get feedback from those who choose to leave the application -- but quitting an app doesn't necessarily signify that; it usually just means the user is task-switching. If you want the "Exit voice" you should attach this to a "delete my account" workflow, or equivalent.
Asking for feedback is inherently interruptive, and takes a light touch; not least because angering the user in the process of asking for feedback is going to skew your results!