Why should we have an entity called "the state" that steals money from people to fund "public services"?
Because that's what civilization means.
Human nature is such that there is always a government of some sort, even if it's not called that. And since it exists, it has enough power to do things for the good of all, if it so chooses.
Consider one person alone: His (we'll assume male) needs are food, water, and shelter. Shelter and water are relatively easy (assuming a good climate), but food requires either hunting, farming, or gathering. Gathering is easy (given knowledge and a decent amount of edible plants around), but requires spending a lot of calories to find small amounts of food. Hunting is hit-or-miss, and very dependent on the animals around you. Farming requires staying put for a long time and putting in a lot of effort before you get any payoff. None of these three will satisfy all of a human's nutritional requirements alone, but time spent on any of them will take away from the others. Plus, there are seasonal lean times that he'd need to preserve food for, even in the best climates. It might be possible for one person to survive this way, but it's not going to be easy. It certainly won't leave time for many luxuries like clothing beyond raw hides or tools beyond wood and stone. Plus, even if he does gather enough food to survive for a time, he's always one injury or illness away from starving to death. Additionally, he has no way to procreate, so he'll just die in the end.
So lets give him a helper. Assume a female, to solve the procreation issue. One of them can hunt or gather while the other farms, or they can both go out and bring more back. With two to split up the chores, they can preserve more food, make more crafts, and so on than either one alone. You do need double the calories as before, but because you can be more efficient with your labor divisions, you can probably manage it. Having a kid will increase the basic requirements and decrease the available time to do things, but eventually the kid can help out, if you can feed it enough, and it doesn't get sick and die (thereby wasting all the resources it consumed).
But what happens when one of them says "It's raining. I want to stay inside and salt meat. You go hunt." and the other one disagrees? Who wins? And then what if the hunter comes back and says "I'm having steak tonight, but you don't get any since you didn't help." Obviously, the other one will disagree. Who wins? Or, conversely, the hunter comes back and then the one who stayed behind knocks them down and takes the food for themselves. Who will prevent that?
Deciding "Who wins" is the core function of a government. It may be as simple as the strongest person threatening everyone else to get what they want, or as complex as a modern multi-level democracy. But humans will always generate some method of group decision-making.
So why listen to the government? Why not just disobey or leave? Generally, you can. Walk away from the clan and found your own. Emigrate to a new country. But either you're moving into an existing group's government's area of control, or you're back in the "one man" scenario. You can't trade with anyone, even if there are other people who would trade with you, because they could just as easily shoot or stab you and take your goods, because there's more of them than you. And you certainly can't buy anything, because you're not a member of their society, and thus there is no shared currency.
Ok, so you can't leave. But why not stay and just ignore any rules that you don't like? Well, then the government will need to decide what to do with you. If it's the local strong guy, he may beat you up. That's no good. If it's the king, he may have your soldiers cut your head off. That's also no good. If it's a democracy, the police will arrest you and take you to jail. That's still no good, although you're at least still alive.
Of course, if you're strong enough to successfully fight back against the enforcers, you might be good... but then they may send more. And more. You have to sleep some time. And there's no one to watch out for you when you are asleep, so you'll have to hide. Which means you can't farm, and have to be extra careful where you go when you're hunting or gathering, or they'll find you. And now you're in the "one man" scenario, except that your life is more at risk.
Or, you can take power away from the government and form your own. Beat up the strong man, and now you can beat up anyone who doesn't do what you say: You're now head of the clan. Get some friends together and defeat the enemy soldiers: You've just had a revolution. But now you're the government, and have all the problems of making other people listen to what you say.
So, all that said, we have a government, and it can enforce it's decisions. Why do "public works"? Why collect taxes? Well, if you're ruling enough people, you can't go around beating them up yourself any more. So you need to pay someone to do it for you (i.e. those soldiers). And that requires money (or otherwise providing for their needs). So you take all the money and valuables away from everyone and give them to your friends: You're a dictatorship. Or you take it all away and spread it out equally to everyone: You're a socialist. Or you only take some of it, so people can keep some of what they've earned: You're a capitalist.
But you need to keep the people happy, or they'll get together and overthrow you. So you spend some of the money you've collected on things that improve everyone's lives. Roads for moving things around. Fresh water and sewage systems so people don't get sick. Entertainment, to use up idle time that might otherwise be spent plotting to overthrow you. All of these public works then make people more productive, which means more growth, which means more power for the government, compared to other governments. Eventually, you end up with a Rome, or a USA, or other superpower.