Still, some people simply are evil - even if they don't see themselves that way, it doesn't change the fact that THEY ARE.
Yes, but that's exactly the point -- that even the most evil people rarely recognize their actions as evil, so they don't
call themselves that. They convince themselves that they're in the right, that they're naturally superior and entitled to win at any cost to others, that the ends justify the means, etc.
If you look at the most truly good and caring people in the world, like Mahatma Gandhi, they usually see themselves as terrible sinners, as screwups just struggling to do the best they can. Whereas the most evil people in the world, like Donald Trump, tend to assume they're the greatest people in history and everything they do is absolutely right and good. Because you can't be a good person until you recognize your own capacity to do wrong and strive to become better. People who deny their mistakes just double down on them rather than correcting them, and thereby become worse.
So it's just dumb writing for an evil character to say "I am evil." Anyone self-aware enough to see evil in themselves is probably basically good, or at least on the way toward making themselves better. A genuinely evil person would deny they've done anything wrong, would rationalize their actions as justified and right. The much better version of Dr. Smith (or June Harris) in the Netflix
Lost in Space demonstrated this quite well. She had an excuse and a rationalization for every misdeed, and she couldn't really redeem herself until she admitted she was the perpetrator of wrongdoing rather than a victim of circumstance.
And that's another thing, though -- neither TV version of Smith
was truly evil. The original may have been written that way at the very start, but that wasn't sustainable in a regular character, so he quickly became less a villain and more just a profoundly flawed person, someone who had no genuine malice toward anyone else but was just so fundamentally cowardly and selfish and dishonest that his actions often proved harmful to others. And June "Smith" was much the same in a more nuanced way, not wanting to hurt others but being willing to sacrifice them to protect herself if it came to that. Both were more multifaceted, interesting characters than Gary Oldman's "I'm so evil I actually call myself evil" version of Smith.