doesn't work half the time
Priests are in most cases human, and humans are in most cases incapable of witholding a secret for a lifetime.
There is a ton of situations in which priests broke that promise for one reason or another, although you could argue that they are more likely to meet a repercussions of it than a psychiatrist would be.
Technically a priest is not allowed to disclose your sins even if he believes that you are a danger to yourself or others[Although again, in most cases they will probably just tip off the authorities if they get concerned]. A psychiatrist is legally bound to report anything criminally concering
So, if you have a bateman-esque dark thoughts they are likely to get leaked in both scenarios, the only difference being that a psychiatrist has been actually trained how to help you with mental stuff, a priest studied one book for five years and then repeated random excerpts from it for another ten.