I’m a bad boy… bad at everything.
On a more serious note, a bad boy is rebellious above all else. He doesn’t follow the established order of things. This can go multiple ways, depending on the cause and manner of his rebellion. There are bad boys in fiction (not so much on Episode) who push back against perceived and actual injustices. There are also plenty who are more like rebels without a cause, or at the very least acting out for personal/emotional reasons. There’s also a big difference between breaking unfair rules, a little talking back, and the occasional fight to defend someone weaker and things like gang violence.
They become irredeemable when their behavior becomes unnecessarily violent or especially if it becomes abusive, regardless of whether their reasons. I’m not a fan of the trope, especially as it’s written on Episode, for that exact reason. If I were to write a “bad boy”, I’d give him realistic motives and just not romanticize genuinely awful behaviors.
A lot of teenagers are drawn to bad boys partially because they’re almost expected to (seriously, the media shoves this archetype down every teenage girl’s throat from a young age, regardless of whether they’re actually attracted to men or not; the whole “everyone likes a bad boy” thing gets pretty weird when you consider how much that attraction is expected). It also happens because adolescence is a time of budding independence when people are most likely to be drawn to taking risks. It’s common for people to be attracted to the potential danger of a bad boy or, more recently, bad girl. It becomes problematic when some people can’t distinguish rebellious behavior from outright violence or fantasy from reality.