When I learned this in ulpan a dozen years ago, instead of téva טבע, the word was אופי ófi, which means character. I'm guessing that Duolingo doesn't want to confuse us, but because of previous training I feel funny about using טבע for someone's character traits. Thoughts?
I can see what you're thinking of, but it's hardly a necessary link. Keep in mind that Hebrew assigns grammatical gender to all sorts of living and inanimate things, not just people. Consider that if you go into the kitchen and see a knife, it's not necessarily a murder weapon; similarly, this phrase need have no negative connotations.