Connor is forced into conflict with his society for the simple reason that he doesn't want his body parts and organs harvested for someone else. In the society that Connor lives in, abortion is illegal. That sounds like a good thing to the pro-life supporters. The pro-choice supporters do not like it. So to appease them, the government allows "unwinding" of children -- specifically teenagers. Any child between the ages of 13-17 can be retroactively aborted through the process of unwinding. Society supports this concept for the most part, because it is argued that 100% of any unwound child will continue to live on in a divided state. It's also stated that an unwound, divided child is statistically more likely to achieve great things, because their body parts are a portion of many more people.
Children that are signed over to be used in the unwinding process are turned over to the state to live in Harvest Camps. Harvest camps exist to care for the soon to be unwound child while organ recipients are found. The children are also monitored closely, so that their body parts can be assessed for future sale prices.
Connor's parents have signed Connor over to be unwound. He's a bit of a troublemaker. His parents are tired of dealing with him, so they have agreed to have Connor unwound. Connor doesn't want to go to the Harvest Camp and be unwound, so he attempts to escape. He is successful in his escape, but in doing so Connor has gone AWOL and become an enemy of the state. It's not Connor's choice to be in this situation. He's been forced to find a way to save his life, and that means being in conflict with the rules and regulations of society.