Like most superheroes, Daredevil has a code against killing. It’s extra important for him since he’s a lawyer and a Catholic, meaning murder goes against all his beliefs. Usually, superhero stories explore heroes killing via Trolley Problems; if you kill one criminal you’ll save other people later. That’s the Punisher’s logic. but Zdarsky opts for something different by having Matt break his code unintentionally. While foiling a robbery in issue #1, Daredevil accidentally inflicts a fatal injury on one of the three criminals, Leo Carraro. Zdarsky has his cake and eats it too; he preserves Matt’s integrity but can explore the ramifications of Daredevil’s actions with a sharper-than-usual edge.
Matt is wracked with guilt when he learns what happened. Daredevil also gets both the law (NYPD Detective Cole North) and other heroes (Spider-Man) on his back. Only one person is congratulating Matt — Frank Castle. The Punisher’s ethos is killing as the solution, befitting a former soldier, and he has chastised Matt for his impermanent methods more than once.
Unaware that Carraro’s death was manslaughter, not murder, Frank is happy that Matt has “seen the light” and saves him from being arrested by North. Matt, who considers Frank a psychopath, is disgusted with himself; their encounter is what finally gets him to confront his culpability. The guilt never leaves him and, eventually, he agrees to accountability via a prison sentence (though due to some legal technicalities, it is Daredevil who serves the term, not Matt Murdock — he even gets to keep his mask). Elektra becomes Daredevil in the imprisoned Matt’s stead.
After this one-off fight, the Punisher drops out of the run and stays gone for a while. However, his presence in issue #4 opens up the thematic can of worms that Zdarsky plucks from as the story goes on.