A number of reasons why I object to the Death Penalty:
1. Possible miscarriages of Justice.
2. Doesn't really do anything to tackle the problem of crime, not even as a deterrent.
3. To reduce the danger of point 1, need to allow the condemned plenty of chances to appeal. This drags the process out and is ultimately more expensive.
4. As was suggested elsewhere, a death penalty would discourage guilty pleas, unless there was an agreement that pleading guilty would lead to a life sentence and not a death sentence.
5. Perhaps more people would plead guilty to avoid death sentences, but they might be co-erced into doing so to avoid the risk of death if found guilty. Again, see point 1.
6. No chance of rehabilitation if the criminal is dead.
There are probably others, but these are the main ones that occur to me. I can completely understand why you would want to bring back the death penalty. But I still think it is the wrong thing to do so.