I'm not sure you understand what "rational" means. It's not the same thing as good, or moral, or right. It means that decisions and actions are guided by reason, facts, and logic...not emotion or value judgments. I don't want to live in a world where everyone exclusively behaves rationally and entirely without emotion, but you simply can't state that "if you start something, finish it" is rational. If it were, it would read more like "finish something if it's worthwhile to do so".
As far as how it's worked out for me? I've quit things both when I should and shouldn't have, and stuck with things under the same circumstances. Some decisions were emotional reactions, and some were made rationally. Some turned out to be good moves, others mistakes. Overall, rationality has served me far better than the alternative...and even when I've turned out to be wrong, I'm infinitely more content with decisions I make that are based on clear, logical thinking rather than doggedly adhering to some belief that quitting is inherently wrong. If that's "part of the problem" to you, so be it.