Your mistake is using "Log in with Facebook" on a mobile device.
Since neither iOS nor Android have any kind of trusted UI, there is no way you can be sure if you are logging into Facebook on an app, or just giving that app your credentials for them to do as they please.
Until iOS or Android get trusted UI for these usecases, I suggest using browsers on windows/Mac/Linux where you can see the in the address bar which company you are giving credentials to, and can't as easily be faked.
If you must use a mobile device to log into Facebook via a third party app, I suggest using a new Facebook account each time.
Since neither iOS nor Android have any kind of trusted UI, there is no way you can be sure if you are logging into Facebook on an app, or just giving that app your credentials for them to do as they please.
Until iOS or Android get trusted UI for these usecases, I suggest using browsers on windows/Mac/Linux where you can see the in the address bar which company you are giving credentials to, and can't as easily be faked.
If you must use a mobile device to log into Facebook via a third party app, I suggest using a new Facebook account each time.