"Due"? You are not entitled to take money from your neighbors' wallets for your own enrichment. It's theft of property/labor. It's a form of partial enslavement (they work, not for themselves, but to make somebody else richer). Therefore it's a violation of basic individual rights. You have no right to take from others.
I'm European. I have never met a person who has gotten rich, or even well-off thanks to welfare benefits. We pay taxes to uphold a society; roads, police, hospitals. That we also pay other things, like child-, education- or unemployment-benefits seems a good thing for me. After all, even if the children aren't my own, they still grow in the same society as I do. It is my gain that they get a high education and the pay check to go with it... because once they are that far, I'll be drawing my pension and and all sort of state benefits. It is better that my home country is the homeland of engineers, doctors and other highly educated people (with of course plumblers and salesmen and whatever else you need to keep a functioning society; but even they need to be well educated to do their civil duty and vote wisely).
Nobody should be in worse position because their father was a drunk or they had no savings for education. And of course, none of this is free. They will pay it back, once they enter the working force. That's the deal. Everybody knows it. And doctor still makes several times more than taxi driver; just a bit less than they do in America. To paraphrase you; if you don't like it, you can move out. Passports are readily available and the world is open at your feet. This is no Soviet Union.
We are in this together. Sure, everybody could just take care of their own life, their own immediate surroundings. I have sometimes thought that part of the reason Americans drive everywhere is because they don't connect with the places between the places important. Why should roads have sidewalks when I have a car? Why have public transport? But that limits alternatives; maybe one day you want to walk to a store only to find out you can't; or take a bus to work only to find out there isn't one. And if you have kids, how are they going to get anywhere without you driving them? Few of us can afford taxi all the time.
Similarly, I pay for many things that I don't need; I pay for schools, daycare and doctors. Even as I am single and have no kids, even if I'm healthy as an ox. But maybe one day I shall have kids, and one day I will be sick. It is good to know that when that day comes, it is not the end of the world. That there's somebody in the bureaucracy who already thought of my kid. That my child can walk to school. That he gets education no matter how I screw my life over. And maybe I make less money (though who knows? American taxes are surprisingly high even before insurances and whatnot), but I can afford to buy everything I need. I don't really feel like I'm worse off than the (incredibly well off) characters in your TV-shows, even if I'm not a secret agent or a doctor or a cop with million-dollar settlement.
