What misunderstandings? They both perceived the other as being a danger to others. Batman's belief was based on a mix of his PTSD and concern about the future threat Superman posed. There's no way to convince Batman that Superman won't be that threat one day. As for Superman, he didn't misunderstand. Batman did brand criminals, and one of those branded was put in critical condition as a result of an attack while in prison. He may have believed the second victim who died also died because of Batman, when it was Luthor who made that one happen. However, for Luthor's scheme to work Batman had to brand that man even though he already knew it put the first guy in the hospital. Batman did, so Luthor took advantage, and Superman wasn't wrong to think that Batman was out of line. He was in this movie.
The truth wouldn't have mattered, because that's not what affected Batman enough to change in the end. Knowing Superman had lived a human life and had a human mother and girlfriend wouldn't have made a difference. What ultimately got through to him was a combination of factors happening all at once. 
Superman has to say, "Save Martha. You're letting him kill Martha" to unsettle Batman, and it does because Batman's self-concept is wrapped up in the idea that he's a guy who doesn't let innocent people suffer like he did: he's not someone who lets Marthas die and Joe Chills win. He's not a villain. Hearing that an innocent named Martha needs help, he stops but still holds the spear in his hand. Once Lois is on the scene, more happens to get him to stand down. Lois puts herself in the path of danger, which makes Batman recall his own mother protecting him, and then Lois explains that Martha is Superman's mother. That, combined with everything else that happened previously, is what gets through and makes a difference. It's not just knowing that Clark has a human mother named Martha. Deduction wouldn't have helped in this case.
Facts don't matter to Batman. He doesn't register them as facts or Superman as a reliable source of information. 
No, emotions don't work like that. Emotions always have the potential to override intellect, and intellect can't solve every problem including this one.