Why did the anti-federalist believe that it was critically important for a democratic society to provide constitutional guarantees for free speech and a free press

Well most likely to have the freedom to say what you need to say, like in the news, they report on things they think they needs to be heard by the people, and the people need to talk about such an event. Like somethin' shady the government was doing, that was recently brought to light, the founding fathers wanted the press to always have the ability to bring a greater light to this.