When your body is overwhelmed with too many emotions or a single strong emotion, like anger, it responds in any way it can, like crying. Even though you're not physically hurting, emotionally hurting can be just as painful, so your body responds to that pain through tears. For example, some people scream or say harsh words when they're angry, but crying comes from a profound emotional feeling. The underlying feelings can be sadness, anxiety, frustration, or any other painful emotion brought out by anger, which is why you start crying.
On the other hand, you might start crying when you feel like you can't clearly express what you're feeling. It can be challenging to communicate your feelings, especially if you have trouble with communication. So when you have to talk, it can overwhelm and frustrate you to tears. However, crying can be good because it allows you to release those pent-up emotions rather than suppressing them. In addition, crying when you're angry shows you're in tune with your feelings, while others may have difficulty doing the same. So don't look at it as a weakness. Instead, view it as a healthy way to cope with your emotions.