When someone is 'in the wrong', they are often expected to apologize for their mistake. After realizing he was in the wrong, he apologized immediately.
Pro Tip 2/3
Responsibility Acknowledged
Acknowledging being 'in the wrong' can show maturity and willingness to take responsibility. She admitted being in the wrong and promised to rectify her mistake.
Pro Tip 3/3
Negative Feelings
The phrase may evoke negative feelings and imply guilt or responsibility for a problem. They argued fiercely, each claiming the other was in the wrong.