Real debates have an 'offense' and a 'defense' side. The 'offense' team presents a case, as to whether the death penalty should be abolished, or whether it should be kept, or whatever. The 'defense' side doesn't present a case, it rebuts the offense's case. Sometimes offense and defense are picked by a coin toss, so whichever side you are arguing, you need to know the arguments for both sides, and the rebuttals to those arguments.
The death penalty is an interesting subject for debates because the arguments -against- it are all logical and rational. The arguments -for- are mostly emotional and political.
Arguments -for- include:
1. Someone who kills someone else deserves to die. (This is sometimes called the 'just deserts' argument).
2. The death penalty deters would-be killers from killing, for fear of being executed (actually this is impossible to prove--its never been shown to be a deterrent, but let your opposition bring that up. It SOUNDS like a good argument).
3. Why should we keep someone alive for decades who's a murderer, housing and feeding him? (actually, the death penalty is MUCH more expensive than the alternate, life without parole, but again let your opponents come up with that.)
4. The Bible says 'An eye for an eye, a tooth for a tooth, a life for a life.' In fact execution is a very old, time-honored tradtition. (So is slavery and no rights for women. 8^) ).
5. If it was good enough for Jesus . . . no, wait, that's not a good one.
6. How would YOU feel if someone murdered your mom or dad or your boyfriend or girlfriend?
7. Here you'd have to do some research. Cite an example of someone who went to prison for a very serious crime, then got out, then murdered or raped someone (Willie Horton is a good example). If he'd been executed it wouldn't have happened.
8. The US system is too kind to criminals, that's why we have so much crime. (Actually this is a totally stupid argument. In the last 30 years we have doubled sentences and then doubled them again. We have more people in prison, per capita of population, than any country in the world. But the 'criminal coddling' argument works very well on an emotional level, which is why you still hear it so much.