You do not need to offer any explanation to your parents. It was rude for them to look through your closets. You would probably truly know if your mother is a snoop or not. There is a high degree of possibility your mother still views you as a child. Some never get over the fact their offspring are entitled to privacy. Some will continually interfere. I would just tell them it is none of their business-period. Frankly, if your mother pushes the issue, I would ask her to leave.
Since you and your brother live together, you may have to level with him. Ask him to respect your privacy. If he cannot do that, then you'll have to consider whether your relationship is worth keeping. Once the Genie is out of the bag, she will not go back in.
Basically you're an adult and will need to make adult decisions.
