There are a million misconceptions about anarchy and anarchism. Presumably this is some kind of typical response you get when you tell people you're an anarchist. With people who haven't thought about what a self-organized culture might look like, you have to go with baby steps. I have had the best results by answering objections like these with redirected questions.
For example, "who will protect us?" can be responded to with: "who do you think protects you right now?" The cops only come after something bad has happened; you know what they say: never one around when you need one. The plain fact is that police don't protect you or your family or your stuff because their job isn't crime prevention, but law enforcement. There's a reason they call it that, and a reason folks in that line of work call it that.
"People will get beat up" can be responded to the same way: "what prevents people from beating you up right now?" Most people aren't interested in beating other people up, but if they are, typically it's in the course of a robbery. Robbery exists because capitalism is based on the unequal distribution of wealth and property. Most robbers rob because they need to get money to pay for other things, like food, drugs, rent, whatever. In a culture that has abolished wealth distribution inequality, the motivations for robbery would be greatly reduced.
If you take apart the objections into digestible bits, turn the question back on the asker in a way that provokes them to think about what their current situation is, then you'll in a better position. But it's important to be confident and knowledgeable. Hope that helps.
