If he had chosen violence the white racist would have gone crazy and would have harmed their views on blacks instead of helping. His calm, respectful, intelligent and non violent methods made him the best role model/leader by example. He was teaching many how to peacefully and respectfully get their voices heard, at the same time he was calm it opened many white people's eyes and kept them calm and rational as well. He was a well spoken and kind man. He had every reason(like every black person then) to be angry and violent. He was a better person than that and realized being calm, respectful and peaceful was the appropriate and best way to help with civil rights. It's a shame everyone couldn't be like him. He didn't hate white people, nor was he anything but respectful to them. Him being the way he was showed many most black people aren't violent, lazy, etc.
If violence broke out the segregationists would have appeared to be vindicated. They would have used the violence as evidence that the races could not peacefully coexist and so should remain separate, "for everybody's best interests". If it had gotten violent they never would have got the support of President Kennedy.