How the Akatsuki members turned all "missing-nin's"? I know why Itachi went rogue, and why he left the village and joined the organization, and I know from other questions and answers why and how the members arrived to the Akatsuki, but I'd like to know why did the Hidden Villages and the Five Great Nation let these kinds of shinobi's to be excluded from their homes, nations, and eventually life?

Just think about it, since almost every member of the Akatsuki once belonged somewhere, and you should be a fool to mistreat and let go of fighters like: Kisame, Kakuzu, Hidan, etc. All of them are powerful warriors, immortals, owning a chakra level like a tailed beast, prodigies of the century, possessors of Kinjutsu's, etc. How come that a Kage isn't able to understand the importance of these kinds of men, especially when "a nation is reflected by the military power it has" and let them go wild, resulting in their exile from their own native villages?
Missing-nins are not shinobi that got exiled from home. That does not happen.

Missing-nins always are shinobi who went rouge and left their villages willingly.

No village would want a shinobi of theirs going away and possibly to some other village spilling all their secrets? Especially not very powerful shinobi who were probably high in the ranks in their respective villages.