Try going to the App Manager, select Facebook, and Clear Cache/Clear Data, then Force Stop. Now try again. If it still doesn't work, it might be a server issue--wait a day or so and try again. Can you still login using the mobile Facebook web page?
I can see in your screenshot that you're using 4g to log in. Have you tried to download and log in through WiFi? Same problem? You never know. The FB app it's full of funny things.