Some ideas for an argumentative speech include school-related arguments like whether the school year should be longer, whether students should wear uniforms and whether a college education is needed to be successful in the workplace. Ethical argument topics could be whether stem cell research should be conducted or whether people should have the right to assisted suicide.
Technology is another topic for argumentative speeches, and whether Internet content should be censored, if technology should be used in the classroom and whether employers should have access to employees' social media accounts are possible topics. Arguing about whether or not immigration should be curbed or whether the death penalty should be used are also possible ideas. The key to writing such a speech is to pick a side and choose strong arguments that support that position, while also bringing up what the other side thinks.