(may contain language...)
Though this is honestly a good summary of everything wrong with BvS
If heroes are going around killing in the way that Batman and Superman do in this film they become 'The Punisher' who is designated an Antihero.
That's not what Superman or Batman were characterised to be, and elements of early comics and The Dark Knight Returns occurred with versions of the characters that do not match or have similarities with the DCCU versions. Deaths also occur in other Batman media, however these are all varying versions of Batman that represent different ages and styles of the character.
I can understand new interpretations, but there is a difference between killing a villain and killing a thug - and in the DCCU, Batman kills hundreds of thugs while letting the main villains live to kill another day.
The writer of the Dark Knight Returns for example believes that blatant murder is justified and i could easily direct you towards 'Holy Terror' a storyline he wrote about Batman that they refused to publish as a Batman story. Point being that The Dark Knight Returns was not the best written and the deaths that occurred in it are because the writer believed Batman had no rules and just killed criminals for fun. The Dark Knight Returns is not really a 'Batman' storyline about his start, its supposed to be his last storyline before he dies because he gives in to killing (Refer back to the 'Red Hood Clip' a few posts above when he talks about how he avoids killing)
He let all the villains from his rogue gallery live. He only killed thugs - so he's still allowing enemies to kill another day, he's just going around murdering the lower level criminals who are just doing what they are told.
Instead he's going around killing hundreds of people in the movie and presumably thousands in his lifetime prior. He doesn't stop any future plans by Lex Luthor, Joker, Harley Quinn, Deadshot, etc...
Killing for Batman doesn't work in BvS because he's up on a high horse believing himself morally and ethically superior to Superman throughout the entire film and his actions are seemingly supported, encouraged and rewarded throughout.
At least with Punisher when he kills, the world looks down on him for it - even in recent shows, people he allies with still realise 'this guy is not a good guy as he's killing people'