Because in this case its the government killing its own citizens.
Medicine is human error, one person with no more legal power than the victim made the mistake. The military kills people but they are not citizens (that sounds terrible and it very much is, I am not excusing the deaths of innocents). With death row mistakes, you have the full weight of the United states government using its power to kill one of its own citizens. In addition, its a long process where the person that dies for a crime they did not commit has to witness their life taken from them one step at a time due to compounding failures. It can also happen to anyone which is the frightening part, a government actor (police, prosecutor, judge, etc) can just decide that you fit the bill and take your life from you.
I am very much in favor of executing the worst criminals but I find myself generally against the death penalty due to the risk of executing an innocent person. I am conflicted and find myself moving back and forth on this topic.