Um, because the law states that if you violate the law and are convicted of that violation, one of the consequences are that you lose certain rights. Voting being the right we are discussing.
Just being the law does not make it right. If you are going to tax someone, forcefully remove their income and livelihood from them under penalty of imprisonment, then it only seems just that they have a say in who represents them. Freed felon or not, they are depending on representatives to defend their rights. Those are representative though who have no incentive to even hear their voices because they are forced to fund a system for which they have no say.
Throw them in jail and ban their ability to vote while incarcerated and not paying taxes, fine. Free them, expect them to rejoin society, be a part of it and contribute to it while denying them any ability to participate in it... that sounds wrong.
It was lack of representation in Parliament which led to the Revolution. I just find something abhorrent about taxing a "free" man but then denying him a say in his gov't. If he is free he should be free, with everything that goes with it. If he is too dangerous not to be free he should not be free. It's that simple.