Martin Luther King was not averse to negotiated resolution of conflict. But despite his strategy of non-violence, he did not exactly renounce more aggressive and adversarial methods either. In fact, the strategy of non-violent resistance was deliberately confrontational, and designed to provoke a violent reaction. That is why it worked. This is shown in the movie when King meets with two SNCC organizers and asks whether Sheriff Jim Clark in Selma was more like Commissioner Bull Connor, whose men had been caught on film brutally attacking protesters in Birmingham the year before, or like Police Chief Laurie Pritchett, who had effectively defused protests in Albany, Georgia, by adopting a restrained policy toward the protesters. John Lewis responds that Clark was more like Connor, and that helped King decide that Selma was the right place to organize protests.
In the end, it was not the court case, or the peaceful protests, or the legislative process in Washington, that caused voting rights to move to the forefront of the nation's priorities in 1965. It was the first attempted march, the one that barely made it across the Edmund Pettus bridge before being met with horrific police violence, that shocked the nation into responding. It was violence that prodded the legal and political system into putting the laws in place that ultimately bring a measure of justice needed to reduce that violence. And it is the tension between the deliberate use or provocation of violence to achieve a movement's goals, and the desire to use the law to create a more just and peaceful solution, that creates much of the thought-provoking drama shown in the movie Selma.