Well that is a stupid statement. Unless you live where there are no police at all, they do protect you/ That is like saying you don't need the government to do anything for you, while driving down the road.
It was short and off the cuff, meant to be spikey and provocative; not meant to be a lengthy dissertation on the subject.
But I have plenty of the latter if they are wanted. We can start with the SCOTUS decision that police are not responsible for the safety of the citizenry.
Any rational person will look at that and realize they'd better make at least some provision for protecting their self.
Then, since Ferguson is on everyone's mind, let's look at how well police and government protected all those businesses that got robbed, looted and/or burned... um.... not so good; how embarrassing.
Do I benefit from the fact that there are police, courts and whatnot? Of course I do. I wouldn't want to live in anarchy, as we have innumerable examples of how that devolves quickly into warlordism and banditry.
However on a pragmatic, day-to-day basis my statement is true: I don't depend on the police to protect me, I depend on me and to a lesser extent on family and neighbors. In the rural area in which I live, 911 is mainly for clean-up and report writing after it is all over.
The plain FACT of the matter is, that it is very RARE for the police to get to ACTUALLY protect someone from direct attack. I know, I was in LE, and I treasure those few times I got to act in that role as gems that made all the rest of the crap worthwhile.
Most of the time, unless a threat is slow developing and called in early, you're on your own. When seconds matter, help is usually several minutes away at least.
I was annoyed by the statement in the OP quote that "People need the police to protect them." In a sense yes, we need an orderly society in order to have a functional society. The rule of law is preferable to the rule of unleashed force.
But frankly, the police need the support of the citizenry just as badly if not more so than the reverse. Policing is almost impossible in neighborhoods where nobody cooperates with the police... which is what makes so many neighborhoods in Chicago and Detroit places of extreme crime and violence.
If you want a peaceful neighborhood, the best place to start is with people being prepared to defend themselves and their homes against criminals; neighbors willing to watch out for each other and call 911 when they see criminal activity; and a police force people can trust and work with.
The worst places in America typically lack all three.