Since the early episodes of "Castle," fans have learned that everyone connected to Det. Kate Beckett's mother's murder has to die. Characters connected with the original murder and with the investigation into it have died. Eventually, the assassin who shot Kate will need to die, and it would be fitting for Richard Castle to be the one to kill him.
In the season finale, Kate finally realized that all she truly needs in life is Rick. By turning in her resignation, she has made a statement that finding her mother's murderer is secondary to her need to be with her partner. Remember, it was her drive to bring the murderer to justice was what caused Kate to become a cop and to become the best possible investigator she could be. She has symbolically walked away from her original drive so it would not be her place to bring this evil character his just deserts.
Esposito, Ryan, and Gates
While Detectives Ryan and Esposito are close to the cases involved with the assassin, it would not be fitting for them to bring the assassin down. They do not have the personal connection with the case like Kate or Rick would. Detective Gates could not be the one to bring the assassin down as she does not have a direct connection to the case at all outside of the fact that her predecessor was killed for being too close.
In the closing moments of the season finale, we saw Mr. Smith being confronted by the assassin. The creators could cause the man, who has secretly helped Rick keep Kate safe, kill the assassin in front of him, but this would not help Kate to finally achieve her original goal in life. Even though Beckett has walked away from her responsibility, it has been written into the show that taking care of everyone responsible in any way for her mother's murder is Kate's destiny. In traditional stories of a character overcoming great odds, the main character can only be progressed by those they love.
With the introduction in the previous season of "Mr. Smith," and the revelation of how Rick has been trying to protect Kate while secretly investigating the murder of her mother, we know Rick has the strongest drive for catching the assassin aside from Kate. In realizing that she needs Rick, Kate has set up a statement in the story of how she needs Rick to complete her and how she needs him to help her complete her life's work.
Rick intertwines into her destiny and will also need to do something to prove how he will go to any length to keep her safe. Confronting and killing the assassin would be the perfect profession of his love and his ability to keep his partner safe. Once the assassin is out of the way, Kate can focus on finding anyone else connected with the murder and bring them down, as well.
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