Why don't people admit errors or wrongdoing?

Because people don’t want to face the consequences? Simply saying “I’m sorry” generally does not absolve you of any responsibility. If someone screws up on their job, they still might have cost people a lot of money and agrivation. It might even cost lives, depending on what kind of job it is. A simple “oops” might not cut it.

It takes integrity and strength of character to admit when you are wrong.

Thats why I never do it, at least.