If you support the death penalty then you believe either:

• The government’s judgements are infallible and it would never falsely execute an innocent person, OR
• You are okay with the government executing an innocent person.

I definitely don’t think they’re infallible, as there are loads of cases where people are exonerated only after serving decades in prison, or after their death. And I’m definitely not okay with the government executing an innocent person.

Then, if you somehow aren’t satisfied with that, you can make pragmatic arguments including how implementing the death penalty costs more than life imprisonment.