It's not effective - there is plenty of evidence it doesn't reduce offending rates.
It's not cost effective - it costs the public purse more than a life sentence.
No conviction is 100% safe. A wrongly convicted life prisoner can be release, a corpse can't.
It reduces conviction rates, because some jurors are reluctant to participate in state murder even if they're certain the person is guilty.
It's not logical - 'killing is wrong, so we'll kill you for it' makes no sense. It encourages people to think murder is sometimes justified - see point 1.
It is not a power that should ever be given to the state.
Permit this government to kill murderers, and the next could extend it to sex offenders, then where are you if abortion becomes included in murder and adultery becomes included in sex offences?
It involves everyone in the justice and prison system in the death. Jurors, prosecutors, judges, prison officers, police, as well as the person who actually pushes the button/pulls the trigger/injects the drugs. What type of person would take part if it made them complicit in murder? Are they the people you want running the system - bearing in mind its primary job should still be rehabilitation of the majority of prisoners who have committed lesser offences?
And it's not civilised.