In my opinion "Bad Girls" isn't a song that pits women against each other, it's a song that celebrates all those female characters who got vilified by their writers for sharing the same personality traits as men.
It's not that common anymore but in the past a female lead couldn't be ambitious or confident, those were qualities only a male character could have. If a female character had those qualities, the writer would turn them into flaws and she would become the villainess.
That's what Bad Girls by Lee Hyori is about, the unrealistic & oppressive standards men push on women through fiction.
You may think "OK but she didn't have to put down other female characters in her lyrics for that" But if you pay attention to the lyrics you'll notice that she's actually taking a jab at this unattainable female ideal.
No woman is perfect enough to be called a "an angel".
With those lyrics Lee Hyori is attacking those standards that force women to "pretend not to know when [they do] know", to "love innocently" and to be sexy but not too much either ("Show just a little skin to be sexy")
Compared to those unrealistic female leads written for men, Lee Hyori much prefers the villainess they despise. And I agree, it's better to be the "Bad girl" in their stories than to force yourself to try satisfying their standards.
I used this song for my edit because I know that all those old sexist writers would be fuming if they ever saw the female characters of Arthdal Chronicles. They are all "bad girls" because they are all women who are written the exact same way as men & aren't vilified for it.
"But what about Taealha?"
She's isn't vilified for being an ambitious women ! She is a villain because she is an overambitious human, just like her male counterpart Tagon & many other male characters (Mihol, Asa Ron, etc) No double standards here !