The appropriateness of your mom's reaction depends on various factors, including cultural norms, family dynamics, and individual personalities. People have different preferences when it comes to household chores, including how they prefer dishes to be washed and whether or not they use a dishwasher.
It's possible that your mom prefers to use the dishwasher for various reasons, such as saving water or time. If she didn't communicate her preference to you beforehand, it might have led to her frustration when she saw you hand-washing the dish instead.
In such situations, open communication is essential. If you and your mom have different approaches to dishwashing or any other household chore, it's helpful to discuss it calmly and find a compromise that works for both of you. Perhaps you can agree on alternating between using the dishwasher and hand-washing, or you could take turns doing the dishes based on your individual preferences.
Ultimately, understanding and respecting each other's perspectives can lead to a harmonious living environment. It's also important to remember that people have different habits and ways of doing things, and sometimes misunderstandings or conflicts arise, but addressing them through open dialogue can help resolve the issues.