How to make an app forget my details for good?

So basically, I've got this app in my iPhone 5c and the only way to use it is by "logging in with Facebook" which I did.
This was two weeks ago.
Now I need to use this app with another Facebook account.
I've signed in with the new account onto Facebook (the app) and messenger as well. Still when I "log in with Facebook" it logs in as the old account.
I have even tried to delete the app and install it again and still the same.
Any ideas?

The reason what you are trying to do won't work is because you arent allowed to have more than one facebook account - that's against the rules

Its Not Gonna Work With Your New Facebook Account Because Facebook TOS Terms Of Service States That You Are Not Allowed To Have More Then 1 Facebook Account If You Make A Another Facebook Account Facebook Can Easily Detect It And Facebook Detected That Thats Why Its Not Letting Your Other Account On

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