Why would you not have Connor (from Neal Shusterman's Unwind) unwound?

I would not have Connor unwound because it is murder.  

The society Connor lives in thinks that an unwound child is still alive, but the child is alive in various pieces. That thought has become commonly accepted, and the headmaster is shocked when Risa suggests her unwinding is the equivalent of death. She tells Risa,

Please, Miss Ward. It's not dying, and I'm sure everyone here would be more comfortable if you didn't suggest something so blatantly inflammatory. The fact is, 100 percent of you will still be alive, just in a divided state.

The citizens probably believe this lie because it is stated in the "Bill of Life."

The process by which a child is both terminated and yet kept alive is called "unwinding."

Chapter one even begins with an Unwind stating he believes that he will actually get to live on after being unwound.

I was never going to amount to much anyway, but now, statistically speaking, there's a better chance that some part of me will go on to greatness somewhere in the world. I'd rather be partly great than entirely useless.

No matter what the society calls it, though, unwinding is murder. I believe that because I believe abortion is murder, and the Bill of Life states flat out that unwinding is a "retroactive abortion."  

Other than my moral stance about unwinding, I would not want Connor unwound because he is a decent person. I will admit Connor has problems with authority figures, but that doesn't mean he should be killed. Connor wants to do things his way without causing anyone else any problems. Contrast him with Roland, who will hurt and betray anyone who stands in the way of his goals. Connor is not that person. He knows right from wrong, and he values human life. His rescue of the storked baby is solid evidence of that fact.  

Connor is also an extremely skilled teenager. He might not be a college-bound student, but that doesn't mean he should die. Once he is at the Graveyard, Connor shows a natural propensity for fixing broken things. He's a great mechanic. The world needs people with those kinds of skills. Connor should not be unwound because he is more valuable to his society as whole person rather than in pieces.