It depends on who is the person in the wrong.
If it's a child, then it matters.
If it's someone I care about, family or friend, then it matters.
If it's a coworker trying to convince another coworker to have an abortion, then it matters.
The list could be longer if I thought more, but I'm tired.
It also depends on the subject.
If the subject is important, like abortion, then it matters.
If the subject is meat on Friday, who cares.
It also depends on the character of the wrong person.
If it's someone who might be open to discussion, then it matters.
If it's someone whose brain is shut tightern a drum, then it's useless and you are correct: it's enough that I am right.
What if they feel as strongly about it as you do, but they think you are wrong?
What if they feel as strongly about it as you do, but they think you are wrong?