When you combine them, 发 (fā) + 脾气 (píqi) literally means “to send out one's temper.” This creates a vivid image of anger erupting from a person.
In Western cultures, expressing anger can sometimes be seen as being assertive or honest. However, in traditional Chinese culture, which places a high value on social harmony (和谐, héxié) and “face” (面子, miànzi), a public outburst of anger is often viewed differently. To 发脾气 is generally considered a sign of immaturity and a lack of self-control. It can cause both the angry person and the recipient to “lose face,” disrupting the harmony of the group. The traditional ideal is often to practice 忍 (rěn)—to endure, forbear, and maintain a calm exterior, even when feeling frustrated. Therefore, while 发脾气 happens in China just as anywhere else, it's often more restrained or confined to private spaces, like within the family. In a professional or public setting, it is highly discouraged and can be damaging to one's reputation. Understanding this helps explain why a Chinese colleague might seem reserved or indirect when they are upset, rather than confronting the issue with an open display of anger.
发脾气 is a very common term used in everyday, informal Mandarin.