Why some stories just don’t want to be written

Occasionally I have great ideas. It doesn’t happen too often, but when it does, it’s a very nice feeling.
Once I had an idea for writing a story. I would write about a false prophet, a man whose terminal cancer gets inexplicably cured and who is consequently propelled into becoming a sort of Californian-style guru. In my mind the whole thing was going to be great: I could just imagine him, doubting himself, unsure as to whether he really had anything useful to say, unsure as to whether to tell others that their cancer could be cured too. And all the while money would be pouring in as if he’d just woken up inside a Monopoly game.
The problem: this story just did not want to come to life. I tried using different angles. Would it work better as a first person thing or coming from an omniscient narrator? Could it be that the language was too formal? Not formal enough? Whatever I did, a plastic cut-out of a story stared back at me, mocking my writing skills. I gave it up.
Contrast this with other stories that might not be great, but desperately want to hatch and become part of the universe. Sometimes characters wake me up in the middle of the night, wanting to continue unfinished conversations. Sometimes they bother me and disturb me until I commit to paper what they want to do and say, and only then will they be appeased enough to let me get on with something else. The question is: Why do some stories not want to be written?