Henry Cavill is right about Superman killing General Zod in Man of Steel. Recently, Cavill spoke about it in an interview with the Hollywood Reporter, where he explains how it is such a powerful moment for the character. Given the direction Superman took in Zack Snyder's films, he makes a great point.
Throughout Snyder's trilogy of DCEU films, Superman goes through a character arc of trying to find his place in the world. Both Man of Steel and Zack Snyder's Justice League, he is revived by his fellow team and returns as a hero fully accepting of his identity.
Henry Cavill's comments about Superman killing Zod in Man of Steel are correct because it encapsulates Superman's entire DCEU story. Zack Snyder develops a very different version of the character than the one fans are used to. The arc Superman goes through requires him to experience real personal growth before becoming the true Man of Steel. In the aforementioned interview with THR, Cavill speaks briefly about what the final scene with Zod meant to him and the character of Superman in Man of Steel.
"The killing of Zod gave a reason for the character never to kill again. Superman falling to the ground and screaming afterward — I don’t think that was originally in the script, but I wanted to show the pain he had. I did far more emotional takes they didn’t choose; tears were happening. He just killed the last remaining member of his species. That’s the choice he made in that moment, and he’ll never do that again. There’s an opportunity for growth after that, to explore the psyche of Superman as a deep, seemingly invulnerable god-like being but with real feeling on the inside."
In Man of Steel, Superman spends most of his life never being able to discover the extent of his powers. This is because every time he tried to do the right thing, Jonathan Kent would tell him that he needs to hide his true strength. While this came from a place of genuine concern for his adopted son, it also led to Superman never really knowing what he's truly capable of. As such, when dealing with a threat like the Superman villain General Zod, he naturally is incredibly inexperienced. When faced with a split-second decision that means the life or death of an innocent family, he is forced to kill Zod because he couldn't think of any other way that wouldn't risk more lives. Bearing the toll it takes allows him to know what's he capable of and what he can choose not to do going forward.
Killing Zod in Man of Steel allows Superman to experience the growth Zack Snyder intended for this version of the character to take in the DCEU. What Henry Cavill tells the Hollywood Reporter shows he understands that. It also makes it disappointing that audiences may never get to see this Superman again, as Cavill's hopes for the Man of Steel show the character was coming close to fully realizing his true potential.