It is not possible. See this link:
https://developers.facebook.com/docs/authentication/
To quote from that link:
Desktop Apps
Our OAuth 2.0 implementation does not include explicit desktop app support. However, if your desktop app can embed a web browser (most desktop frameworks such as .NET, AIR and Cocoa support embedding browsers), you can use the client-side flow with one modification: a specific redirect_uri. Rather than requiring desktop apps to host a web server and populate the Site URL in the Developer App, we provide a specific URL you can use with desktop apps: https://www.facebook.com/connect/login_success.html.
The reason that this is not possible is that facebook uses the OAuth protocol. More details on the OAuth protocol can be found at:
https://www.rfc-editor.org/rfc/rfc5849
The fundamental motivation behind OAuth is so that the resource that needs authorization does not need to know the credentials/identity of users.
What you are proposing (taking in the clients username/password) goes against the fundamental tenets of the OAuth protocol and you cannot (at least legally) achieve this with facebook.