This isn't just true in public discourse by the way. It's true in proposal/grant writing, legal argumentation, or even just arguing with your parents. You should always lead with your strongest arguments, and think very carefully before including any weak ones. Humans are just bad at doing weighted analysis of persuasive arguments. Say you have an argument, with three points, with weights: 0.9, 0.05, and 0.05. Your opponent destroying your two weak arguments is going to convince the reader or decision maker far more than the 0.1 combined weight of the arguments.