Dialogue makes the world go 'round.
Stories don't depend on dialogue, but it makes them a lot more dynamic. Moreover, dialogue is a great tool for exploring your writing voice.
Wherever there is dialogue, there is understanding. And, wherever there is understanding, there is peace. As long as we talk to each other, we are not killing each other.
This is true in any human relation. Whether it's at the highest political level, or at home with your partner in life, dialogue leads to understanding. It's a crucial part of life.
As a result, dialogue is a crucial part of writing, too. We are, after all, writing about life in its many forms.