I get why someone caught with a misdemeanor would prefer the word wrong. In modern times, people will often say that they did something by mistake while making apologies. To do something by mistake means that you did it by accident and without intention. Because it is done by accident, usually you will not know about the mistake until it is done and you are pointed to it. So fast, in fact, that it happened before you even realized you made a mistake. Once you recognize your error, consider what you can do to avoid having that happen again. If you can reframe your mistake as an opportunity for learning, you will be motivated to be more aware and resilient. When we frame our mistakes as opportunities for learning, we are far more likely not to face failure in the long run. It is also really important that we learn from our mistakes, so that we can adjust our responses and do things differently the next time we are in the same situation.