Sounds like the app is crashing. Try signing out of Facebook, and then uninstall both Messenger and Facebook. Reboot. Then reinstall both apps and see if this does the same thing.
If it's still crashing, you might want to check the crash logs (Settings > Privacy > Diagnostics & Usage Data) and see if you're getting a bunch of entries for Messenger. If you see a lot of crashing, then iOS might be corrupted (seems more common if iOS is updated over-the-air, rather than using iTunes).
If this happens, then you'll probably want to backup your device (I prefer using a wired connection to iTunes, because it saves everything) and restore as a new device. This will reload iOS 8.2. Then after restoring the device, you can restore your apps and data from a backup.