This comes from Superman (Henry Cavill) during the film's climax when he's actually fighting — and losing to — Batman (Ben Affleck). Lex Luthor (Jesse Eisenberg) is holding his mother, Martha Kent (Diane Lane) hostage, so he, delirious from the effects of Kryptonite, implores Bruce Wayne to save her. What he doesn't know is that Batman's mother was also named Martha and Bruce screams back, "WHY DID YOU SAY THAT NAME?!" In the end, it's this common ground that stays Batman's hand in killing the Man of Steel, resulting in their ultimate alliance.
It's kind of a silly moment, one that angered fans and lent itself to parody in Deadpool 2 when Wade (Ryan Reynolds) is trying to explain to his girlfriend, Vanessa (Morena Baccarin), why he's home so late. But beyond the humor of the exchange, the real question is why Superman, with all of his god-like powers, couldn't just save his mom in the first place, rather than giving in to Luthor's demands and duke it out with the Caped Crusader. After all, he did it for Lois Lane (Amy Adams) at the start of the movie, when she's being held captive in the Middle East.
Director Zack Snyder answered the question on his usual social media platform of choice, Vero. According to him, there was supposed to be a green screen shot of Superman flying above the city and trying to locate his mother, forced to ignore all the other crimes going on at the moment.
"He flies up above the city and hovers," Snyder wrote. "The camera begins to rotate around him as he hears the cries of citywide crime going on and, as we get closer, he is in pain because he knows if he [tries] to find her this way, he will have to ignore the countless crimes going on in the two cities and the world."
Had this heartbreaking moment been included, Batman v Superman may not have gotten as much flack as it did (though, in tasking Batman to save his mother, he's still ignoring all those other crimes, right?). The decision to pit Superman between his own self-interest and the greater good would have been a really profound character moment for him and the audience.