(Quoting my answer from the Movies SE:)
Apparently this is somewhat explained in the Ultimate Edition:
The theatrical cut made a big deal about Batman branding criminals
with a red-hot bat-symbol branding iron, and briefly mentioned that
inmates in prisons with this brand are quick to be killed by fellow
prisoners… for some reason? It was all kind of vague. In the Ultimate
Edition we see that Lex and company pay one of the inmates to “shiv”
the latest bat-brandee in the prison yard. This is all part of Lex’s
plan to stoke the fires of Superman’s outrage at Batman’s methods.
CinemaBlend expands on this:
Remember Cesar Santos? The criminal near the beginning of the movie
who Batman branded? Well, there was a lot more to his story in the
We already knew that the Bat-Brand was a death
sentence if you're caught with one in prison, but that also makes it a
suitable cover for pulling off a sinister assassination. Anatoli is
seen paying off one of Cesar's fellow inmates, and later, that same
man stabs Cesar to death during recreation time.
Like in the
theatrical movie, Clark is sent pictures of Cesar (by Lex Luthor), but
this time, one of the photos is of his corpse. Clark then goes to
Gotham City to learn about Cesar's death, and while the police aren't
being cooperative, he comes across Cesar's girlfriend and son. She
tells him that the police know the brand means eventual murder, but
they won't do anything about it. Clark wants to help by telling her
story via The Daily Planet, but she retorts that a pen won't stop
Batman, only a fist.
This helps clear up why Superman was willing to
switch from words to force during their later battle.