In the American system of justice the convicted are sentenced to incarceration, ordered to pay restitution and court costs as a penalty for their actions. The objective of incarceration to both punish and rehabilitate the offender. Once these items have been completed the offender's debt to society has been paid. It's only fair that voting a fundamental citizenship privilege be restored.
When you commit a crime and are convicted they no longer have the right to vote. They forfeit all rights as a citizen of United States. Until they are released from prison and rehabilitated they do not have the right as law abiding citizens to vote and take part in the political system.
Felons should not have the right to vote in any election simply because they infringed upon the rights of others and were convicted of doing so. Felons generally know what they are doing is wrong and violates the law. So when the law separates a felon from society, that convict is also separated from the democratic process that chooses our leaders. It simply makes judicial sense because felons can form their own voting bloc to try to influence political leaders.
If you give the vote to those who break the law, then you create an electorate to whom politicians who write those laws may court to gain election. If the felon vote can grant offices to some politicians or cost them to others, then granting felons the right to vote means a weaking of the rule of law.