The difference is that programmers know they will make such errors and thus have developed tools, techniques and a culture that acknowledges the necessity for testing to find and eliminate bugs.
In contrast, I'd wager that less than 0.01% of financial Excel sheets has automated tests, and less than 0.1% has a written test plan. If you confront your typical "work-hard-party-hard" hotshot trader with demands for such, the response is most likely "Testing? I wrote it, I know it works, do you think I'm stupid?"
LOL, seriously? How much software do you use every day that doesn't have bugs? Especially software that only gets used every now and then?
Or were you jsut put off by the phrase "eliminate bugs"? That wasn't meant to imply eliminating all bugs, just those the tests have found. And we all know they don't catch 'em all.