That is a phrase I was raised with and have heard more times than I can count. It's a quick and catchy way to provide advice and it's likely intended it to mean follow your instincts. Still, I suspect it had some unintended consequences.
It may not be this phrase for you (which is attributable to Ben Franklin), because there are plenty of similar proverbs that teach us to run when we're feeling unsure. That may have been a good instinct for our hunter / gatherer ancestors, but it isn't doing us much good today (unless we're talking about something like peer pressure).
These ideas, though well intentioned, may also be training us to avoid anything that makes us feel uncomfortable. Yet there are plenty of worthwhile things that make you feel pretty uncomfortable. Moving to a new city for college can be uncomfortable. Applying for jobs and going on interviews is definitely uncomfortable. Making a cold call to try to get an internship? Scary. Risking financial security to pursue your dream career? Absolutely terrifying.
If it were up to that visceral reaction that tells us to run, we wouldn't try any of those things and we'd miss out on a lot of amazing opportunities. More importantly, we'd miss out on the chance to succeed. Don't let your fears stop you from living your dreams. So, sorry, Ben Franklin, but it's time for an amendment: when in doubt, do it.