The quotation you provide above isn’t about violence at all. It is one of MLK's many responses to the claim, very common in the 1960s, that African-Americans should not be making big public (non-violent) demonstrations and sit-ins, because this would be too socially divisive. Instead, they should somehow push for change in a low-key manner that doesn’t upset anyone.
I strongly recommend reading some histories of the 1950s and 1960s civil-rights movement, it was a fascinating era. MLK was deeply committed to non-violence, he wrote at great length about why he felt that non-violence was the superior method for pursuing the civil rights cause. It was other African-American ideologues who favoured violent actions, and tension arose between them and MLK because of it.