Partner of 3 years won't add me on Facebook?

[*your*dark*queen*]

No, your not paranoid. His behavior is shady and he is hiding or trying to hide something from you. Facebook has a setting where you can hide your relationship status from specific people. He may be passing himself off as single. He's obviously flirting with other women and trying to appear available. If you call him on it I am sure he will say your being insecure, paranoid, stalking him online or something like that. All this tells you is that he is most likely not ready for a real relationship and either enjoys flirting or is cheating or trying to cheat.
You could try creating a fake Facebook page of a single, pretty lady and try befriending him and see what happens.