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 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 Socrates is wrong to classify Oratory as a shameful 'knack.'
In this paper, I will argue against Vlastos' interpretation of Socrates' position in the Gorgias. The texts support the position that virtue is the only constituent of happiness, and this position does not run into the sorts of practical difficulties that Vlastos alleges it does.
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.
Vlastos condemns Plato's position on the sort of regard we have for other people when we love them. In this paper, I will argue that Vlastos is right.