1) Many times it's not that you're lacking in any manner, it's just that there's someone that suited the position better. It's like dating - if you reject someone because someone better came into your life, what do you tell the other person? Usually it goes "it's not you, it's me...".
2) Sometimes I don't know what I'm looking for until I look. Then I get responses and realize I'm looking for the wrong thing. Then when I say no, again, it's not because of you, it's because of me. Sounds like dating again.
3) Finally, connections and personal relationships help. If I don't know you from Jack Adam, then it's hard to provide any sort of useful feedback if I don't have that much useful feedback. If we had a relationship, then I could give you some sort of advice on what would be a better fit for you, make a recommendation to someone else.
Instead of asking "what went wrong", maybe you might want to ask "is there anyone you can recommend or do you think that something / someone else might be a better fit"? You never know whomever else we might know in the space that's hiring. And while we might have found for ourselves a great mate, that doesn't mean you're not dating material. Perhaps we have just the right fix-up for you. Or maybe not.
Just one additional perspective.