Hey there, Hlar33,
Thanks for visiting the Apple Support Communities. I understand from your post that you are being prompted to sign into Facebook Messenger on your Apple Watch, you're prompted to first login on your companion iPhone. I'm happy to help.
First, make sure you're signed into Facebook Messenger on your phone.
Then, see if the information Facebook provides about using Messenger on your Apple Watch helps: What can I do with Messenger for Apple Watch? | Messenger Help Center | Facebook.
If you still are having trouble, go through the steps outlined in the Apple Support article If an app unexpectedly quits, stops responding, or won’t open - Apple Support on both your phone and your watch.
You may also find Facebook's support article I can't log into the Messenger app. | Messenger Help Center | Facebook helpful.
Best.