Everything that happens in your life needs to appear in consciousness in order for you to know about it and, as a matter of personal experience, for it to matter. This includes both mentally internal and external events. As for the mentally internal events, this fact presents an opportunity to look closely at what you're doing with your mind and respond in better, healthier, more productive ways. If you think you can stay angry for a day or even an hour without continuously manufacturing this emotion - by thinking without knowing that you're thinking - you're mistaken. This is an objective claim about the mechanics of the mind. And I invite you to test it. Introspection, particularly meditation, would be the tool you would use to test it. You can learn to not stay angry for very long. This is not to say that circumstances don't matter. They do. But it is your mind rather than circumstances that determine the quality of your mind and, therefore, the quality of your life. This fact explains why some people are content in the midst of deprivation and danger while others are miserable despite all the luck in the world.
While being content independently of circumstances is effectively a super power, it is also objectively important to improve our circumstances. We can become more effective at understanding and acting upon reality by improving our relationship with it. Just like you don't read a book at arms length nor by having it flush against your nose but rather at a distance that allows you an optimal grip on the text, you can learn to have an optimal grip on reality that allows you to see exactly the amount of relevant detail while also keeping a healthy and useful overall picture.
So why train your mind? The basic logic is quite simple: the quality of your mind determines the quality of your life.