If a person is born into a state he becomes a citizen of that state. With the rights he gets he also gets duties. The right to vote also constitutes the duty to oblige to everything the majority rules. If he doesn't like that, he is free to leave the country.
When we think of human beings owing a debt for their life, we are on a slippery slope that may lead to irresponsible and immoral actions such as running a governmental budget deficit that the next generation has to pay for.
This debt is accrued over time. For instance, at birth they are cared for by doctors shaped by the society, transported home on roads made by the society, educated in schools molded after the society, etc.