WARNING: The following contains spoilers for Batman/Catwoman #2, by Tom King, Clay Mann, Tomeu Morey, and Clayton Cowles, on sale now.
Andrea Beaumont just started a war with the Clown Prince of Crime, and she's hunting down his men one by one. She also goes by the name Phantasm, but her victims only know her as an angel of death. Batman and Catwoman are hot on her trail, but the only thing they've found so far is a trail of blood. While we don't know how Andrea and Joker's story will end, Batman/Catwoman #2 makes it clear that it's enough to push Selina Kyle over the edge and shatter Bruce Wayne's final wish of sparing the Joker's life.
Whatever the Joker did to make Selina hold a grudge for all of these years must have been tragic. However justified she may have felt killing the Joker, it stands as one final betrayal to not only Bruce Wayne, but Batman's entire legacy. This act shows that Selina may have loved Bruce, but their relationship was built on a moral foundation that was so shaky not even time could fix it.
While Selina and Joker exchange pleasantries in the first issue of this Black Label series, the second issue makes it clear that one of them isn't going to walk out of there alive. When the Joker goes to fetch two glasses of water, he instead pulls out a long-barreled revolver stashed in the freezer behind a bag of frozen vegetables. While doing so Joker reminisces on the good old days fighting with Batman and Catwoman and escaping with his life, adding that these dances with death always made him feel young.
Joker returns to the living room only to fires several rounds into the couch where Selina was sitting. Selina is standing directly behind him and disarms him viciously with a picture frame. She then begins to beat him senseless while telling him how long she's been waiting for this moment. She tells Joker that she's always wanted to kill for what he did to Andrea Beaumont. She begged Batman to let her do it, but he wouldn't budge. Bruce even told Selina with one of his final breaths to spare Joker's life. But it's clear as Selina takes off her glove and slices Joker's throat open that she never intended to follow through with Batman's final wish.
We learn throughout the first two issues that Selina was working with Joker behind Batman's back. It's not totally clear what they were up to, but it has something to do with a stolen necklace. Elsewhere in the issue, Selina lies to Batman about being with Joker when she broke the so-called unbreakable safe to get access to the golden necklace. If Selina was able to lie to Batman's face this far into their relationship, then it's not too much a leap to see how quickly she would betray his final wishes after his death.
While it may not seem like a big deal to kill the Joker, it's one of the greatest insults Selina could leave on Batman's legacy. If anyone were to ever kill the Joker, it would have been Batman. And if anyone deserved to kill the Joker, it was definitely Batman, but he always refused to sink to his level and break his sacred no killing rule.
This is what always separated Batman and the vigilantes he fought alongside with the criminals he fought with. While Selina may have loved Bruce Wayne, she still couldn't put the relationship before her own sense of self-preservation. Batman sees the best in people and always saw the best in Selina. Batman never wanted Selina to kill Joker because he wanted to protect her from the worst parts of herself. When Bruce died, it didn't take Selina long to revert back to her violent and selfish ways. While Joker is dead at the end of the issue, he has the last laugh at Selina's expense knowing she broke Batman's trust one last time just for him.