This is indeed a great question and a lot of things mold us into what we have become today. I think the two factors you mentioned here have a role to place.
A lot of things combine as the result of what we are today. These things involve the challenges we face in life, mindset, environment, and lots more so it is best to say we are both products of nature and nurture since the presence of both is the key.
RE: Nature vs Nurture: The Factors Shaping Our Identity