These are just samples; you may argue for one of these if you wish, but you aren't restricted to them. Another good place to look is in the list of reading response papers; they give a decent list of topics we've studied and suggestions about things you might want to argue about.
In this paper, I will argue that Socrates in right when he thinks that the only thing that matters of happiness is the health of your soul, but that (contra Socrates) worse people are able to harm the soul of a better person.
In this paper, I will argue that Socrates' objections against Euthyphro's definition of piety as what all of god love does not successfully refute a Divine Command Theory of ethics.
In this paper, I will argue that Polus could (and should) have been able to maintain his thesis that it is worse to suffer injustice but more shameful to commit injustice.
In this paper, I will argue that Callicles' attempts to appeal to nature to support his distinction between 'natural' and 'conventional' justice fail.
In this paper, I will argue that Burnyeat was right: Socrates was guilty as charged.
In this paper, I will argue that Socrates' use of an afterlife myth at the end of the Gorgias is an example of using the sort of shameful oratory he condemns.