There are introspective "me" songs that are quite good. Carrickfergus for example. What you don't care for, someone else may love. I think good songs are ones 1) people want to hear, and 2) people want to sing. As for good songwriters, I agree with 999 (who knows) about being a good listener. It's the same thing with good writers being good at reading and understanding, and good artists being able to evaluate and understand other people's art. Mostly, I think it's the understanding. Being good at appreciating art of any sort doesn't mean one can do it, but I don't know of anyone who is any good who can't understand their medium.

Being good at songwriting means you don't just luck out with a song or two, but do it consistently.