Why does Henry list all the methods the colonists have tried to reconcile their differences with the British for the last ten years?

By listing all the American colonists' grievances against the British, and by reminding his audience of all the efforts made by the Americans to reach an amicable settlement with the mother country, Patrick Henry's trying to ram home his central point that independence is not just desirable, but essential. He knows that many, if not most, of his immediate audience are deeply skeptical of breaking free from Great Britain. So he frames his case for independence in such a way as to make it seem like the Americans have no choice in the matter.
Despite his fighting talk, Henry also wants to present independence as a reasonable option, the rational response to years of British intransigence, arrogance, and contempt. In a way, he's suggesting that the desire for independence is something that's been forced on the colonists by the British themselves and would never have come about otherwise. The Americans tried hard on numerous occasions to reconcile with the British, but each time they were rebuffed, treated with high-handed disdain. Thus the Americans are left with no choice but to go it alone.

Because Patrick Henry knows that the majority of the men attending the meeting of the House of Burgesses are inclined to try to keep negotiating with Britain for better terms for the colonies, he needs to bring as much logic as he can into his argument. By listing all the negotiating techniques the colonies have tried, such as petitioning, remonstrating, supplicating, and arguing and then listing what the British response has been to each of those strategies, Henry attempts to convince his audience that the colonies have exhausted every kind of nonviolent negotiation. Henry appeals to logic and reason to make his point that it would be futile to take negotiations any further. In his mind, the only strategy left untried is to declare war, and that is his proposition in this speech.