"When the debate is lost, slander becomes the tool of the loser(s)" refers to certain people's tendency to turn the biterness and humiliation of losing an argument into personal attacks against the debate opponent and their image.
To slander means to defame, to say false things about someone in an attempt to damage their reputation.
This statement is often attibuted to Greek philosopher Socrates, but there isn't any evidence supporting the fact that he originated the phrase, so it would be best to avoid quoting Socrates in this case, especially in school assignments.