You followed the steps that facebook provides for the creation of a login application?
You need a 'Production keyhash' obtained starting your release keystore:
From comand line:
keytool -exportcert -alias <RELEASE_KEY_ALIAS> -keystore <RELEASE_KEY_PATH>
| openssl sha1 -binary | openssl base64
And add this key on facebook app page options.
More information: [Facebook Docs][1]

[1]: https://developers.facebook.com/docs/android/getting-started/

You followed the steps that facebook provides for the creation of a login application?
You need a 'Production keyhash' obtained starting your release keystore:
**From comand line:**
keytool -exportcert -alias <RELEASE_KEY_ALIAS> -keystore <RELEASE_KEY_PATH> | openssl sha1 -binary | openssl base64
And add this key on facebook app page options.
**More information: [Facebook docs][1]**

[1]: https://developers.facebook.com/docs/android/getting-started/