It seemed like quite a noble rule to live by.
The problem I never noticed was that...I would intentionally NOT START things that I wasn't sure I'd want to finish. Do you see the problem with this? It reminds me of 'Fasting till you get what you want' - the issue with pledging to finish everything you start is that you become AFRAID to try new things, to experiment, to get involved with the unknown.
A great example - these days, I don't finish books I'm not enjoying - because inherently, I just stop reading altogether, unless I pick up something that makes me prioritize reading above other things.
I do however, found that I've replaced it with a new rule: Finish what you COMMIT to finishing.
I frame it in terms of starting a company.
If I committed to finishing every company I'd done work on starting, then I never would have moved past my first idea, and never would have picked up another. Every idea I come up with requires research, testing, discussion, etc - these are the things that go into STARTING it. BUT, if at some point I realize that the market's not there, or the revenue model isn't there, or I'm not inspired by the idea - I lay it to rest, no regrets.
However, the moment that I recruit a partner, that I've pledged that we're in it to win it, that I raise money from other people to fund it - I've committed. I've given my word that I will see this thing through to the end, and it is only then that finishing is a matter of integrity.