King means that those who are in control, never voluntarily give up that control. Whether you consider the English in India, ante-bellum plantation owners in the American South, or whites in apartheid South Africa, those in control do not willingly give up their power.
By implication, King applies this to civil-rights era America. "White" America will not voluntarily give civil rights to "black" America. They will have to in some way be made to give blacks civil rights.
He is basically saying that freedom is not free. To earn it means to fight for it, and when you are on the opposite end, or on the losing end of it, it is highly unlikely that you will be given any sympathy. Hence, you are on your own. If you are then your biggest responsibility is to establish your rights and do everything you can to make your point. It is a historically=proven fact that freedom often comes through war, battle, or struggle. But the prize is well worth it.
What he meant by this is that black people could not just stand around and expect white people to give them freedom or rights. Instead, he was saying, black people would need to stand up and demand those rights.
He was saying that the white people were the oppressors -- they were oppressing black people by keeping rights away from them. He said that a group that is oppressing another will never just quit on its own -- it will have to be forced to quit being oppressive.
So, this was a call to action -- a call for black people to stand up for their rights.