Children know very well that both parents will never react the same way. They feel one parent will listen calmly while the other will just shout. They naturally prefer sharing uncomfortable things with the calmer parent.
A 2006 study observed 276 students from 9th and 12th grades to understand how they share information with parents. Researchers found that teenagers share personal details more with their mothers than their fathers. Trust, a feeling of acceptance, and a sense of responsibility heavily influence how much a child opens up.
We cannot directly apply this teen study to younger kids, but the basic logic remains the same. A child expects mom to talk peacefully and dad to react with anger over a mistake. They will naturally ask mom to hide the mistake from dad. You must understand their fear instead of assuming they want to create fights between parents.