When is the last time you truly screwed something up? Being a parent of a young family means I have plenty of personal examples, but my last professional screwup was not being as insightful with my first app, So Quotable. I really believe it would have taken off had I better understood the market fit.
The real impact isn't if you've made a mistake, though, but what you do after you realize an error was made - especially those, like launching a startup, that do not give you a do-over.
The key is to separate the error from your self. It doesn't mean not taking responsibility when you led your company down the wrong path. Instead, it is understanding that a mistake doesn't mean leadership is not in your DNA.
Brene Brown's modern classic Rising Strong explains why that separation is important:
Shame is a focus on self, while guilt is a focus on behavior. This is not just semantics. There's a huge difference between I screwed up (guilt) and I am a screwup (shame). The former is acceptance of our imperfect humanity. The latter is basically an indictment of our very existence.
The weight you carry from a failure can be interpreted as a learning experience or as a career-crippling decision. The size of the failure and the public reaction can make it harder to see it as the former, but how you interpret it is ultimately up to you.
When we don't take our failures well, we lose more than our self esteem. We also lose our passion for the adventure. As X (former Google X) lead Astro Teller said in a recent TED Talk, "We have this interesting balance going: We allow our unchecked optimism to fuel our vision, but then we also harness the enthusiastic skepticism to breathe reality into those visions."