Why does it take audacity to vehemently deny that you told a lie?

Because if you accept that you lied, people are going to know that your are not honest. All people want to be accepted by society, and lies have bad reputation among others. So, this lacking of honesty will make you vulnerable and possible you could be rejected socially.

paine is arguying that they had tried everything before coming to the conclusion that they needed to fight for their freedom.

argument: "every quiet method for peace hath been ineffectual."

claim 1: "our prayers have been rejected with disdain; and only tended to convince us, that nothing flatters vanity, or confirms obstinacy in kings more than repeated petitioning and nothing hath contributed more than that very measure to make the kings of europe absolute."

claim 2: "wherefore, since nothing but blows will do, for god’s sake, let us come to a final separation, and not leave the next generation to be cutting throats, under the violated unmeaning names of parent and child."

the author develops a cold, and scared tone. making the reader shudder with fear, and suddenly become cold. i'm guessing that he's writing a scary novel, or maybe about a chilly december night.