And in response to their actions not making sense?
This isn't about the characters it is about the Fal'Cie not making sense

The human mind has a reflex against stabbing itself.
Yes, but we can still do it. Even assuming that a Fal'Cie couldn't kill itself there is nothing saying a Fal'Cie couldn't kill another. If they put that one line of dialog in it would have made the story actually make a little bit of sense. Or how about selecting humans that actually want to destroy Coccon?

The Fal'Cie had hundreds of years to think up a way to kill themselves, and the best they can come up with is to give a bunch of humans special powers and hope they do it? Seriously?