Inquiring minds want to know

Can someone explain to me why the liberal left supports abortion, yet is against capital punishment? I never quite understood stood this. Why is it OK to kill an innocent human life, but yet not OK to kill a guilty human life?

A baby, at one point in time, whether at the exact point of conception or at a later point in its development, becomes a human life...a completely innocent human life. The liberal left supports the woman's right to abort...a.k.a kill, this innocent human life. Even if this human life somehow manages to survive this procedure, their book says it's OK to leave the baby alone in a room to die. This human life is guilty of absolutely nothing, other than being in the wrong spot at the wrong time.

Contrast this with a convicted murderer...someone who has made the conscious decision to take the lives of others. Why should this human life be spared and allowed to live? Why isn't it OK to kill this human life? Why should everybody else have to pay for food, clothing, housing, medicine, etc. to keep this human life alive in prison for the rest of it's natural life? If any life deserves to be killed, it would be this one, right?

This just never made sense to me. And is a big reason why I have a difficult time understanding and supporting any liberal agenda.