Why does the Punisher turn down Daredevil's offer in Daredevil: Born Again?

In Daredevil: Born Again, Punisher, aka Frank Castle, turns down Daredevil Matt Murdock's offer because of their perpetual mismatch of ideology. Though they both are vigilantes, their approaches towards the criminal are contrasting. Punisher's way is more direct and lethal, while Matt believes in the justice system and opts for a morally acceptable way. For Punisher, Matt's approach comes with consequences and biases based on the power, class, and race of the criminal.

Secondly, Frank is aware that law enforcement is misusing his symbol in various ways, especially under Fisk's rule. Therefore, his primary motive might also be to re-establish his name. Read on to know why Frank refuses to help Matt in Daredevil: Born Again.

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Here is why the Punisher turned down Daredevil's offer in Daredevil: Born Again

Matt Murdock, while investigating the Hector Ayala case, finds Punisher's symbol in the crime scene and highly doubts the possibility of him shooting the White Tiger. This is because of his one moral principle-- Kill only when he deems guilty. However, Matt decides to reach Frank Castle and eventually asks him to help him find the culprit, which Punisher turns down immediately, saying,

"I do not have time for your candy-a** hero s***!"

Hector was facing trials as a result of murdering an NYPD officer. By the end of episode 3, Matt represents him and gets him released by revealing his identity publicly as a White Tiger. This upsets Hector, but he walks off freely. That is when someone shoots him in the head.

Someone has used the Punisher's identity to attack Hector Ayala. The suspicion strengthens when they get to know that Fisk wants Hector dead. Despite this, Punisher refuses to help Daredevil, highlighting his meek way of dealing with real criminals. Punisher comes with the motive to eliminate criminals, while Matt's process relies on a sense of duty and belief in the law.

Foggy Nelson's death left Matt shaken as she was killed by Bullseye to take revenge on Matt Madrock. After Foggy's death, Matt confronts Bullseye, but instead of killing Bullseye, he waits for the justice system to solve the case. Punisher sees this as a wrong choice as this lets Bullseye live despite the harm he has caused.

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This portrays the complicated plot Daredevil: Born Again is building and the events it will lead to. Indeed, Punisher considers Matt's moral code as rigid and ineffective.

However, Frank Castle will return in Daredevil: Born Again as he is determined to re-establish his name after it was misused by the authority figures, now that he knows about the bullet with a skull logo. He will return to tell everyone who the real Punisher is.