No, people are not choosing emotions. You can show them or not, but it is not true that one "chooses" them.

A popular perspective is that emotions are the result of quick analysis of a situation, trained on survival instincts originally but later mostly pattern matching and beliefs. By observing emotional reactions you can drill down to the underlying belief, and over time adjust to new circumstances. For example, based on this theory, anger is the result of an analysis that determines that something is deemed wrong and it is within your power to change it (or extract yourself from the situation). If it’s judged to be not within your power, the resulting emotion is sadness. And these judgments can be changed to have a different emotional experience - beyond feeling them or acting on them. This adjustment requires to identify the original deep pattern/beliefs, not just surface-level desire to do so. This introspection typically requires third party assistance, available in various therapeutic and coaching settings.