Okay, kiddo, so a loyalty oath is like a promise that someone makes to show that they are loyal to something or someone. It's like saying "I promise to always be on your team and never do anything to hurt you."
Sometimes, people who want to work for the government or go to school have to take a loyalty oath to show that they are loyal to the country they live in. It's like saying "I promise to be a good citizen and follow the laws of my country."
Taking a loyalty oath is important because it shows that you are committed to being a good member of a group or society. It's kind of like being part of a team and promising to always do your best and stick together no matter what.
But, not everyone likes taking loyalty oaths because they feel like it's forcing them to be loyal to something they might not agree with. Some people think that being loyal should come naturally, instead of being required by a promise.