Necessity is the mother of invention in chapter 1 and 2 because the boys need to invent ways to survive on the island.
To “buttress” is to "strengthen or justify." In this case, you want to justify the expression based on events of chapter one and two. The expression “necessity is the mother of invention” basically means that new ideas come from a need. When we have a need, we need to come up with a way to address it.
Chapter one and two sees the boys stranded on a deserted island. There are no adults. Since there are no adults, they have to come up with a leader. The choosing of a leader creates a schism between two factions from the beginning. Ralph is chosen because he blew the conch, and Jack is annoyed because he sees the leader as his rightful place.
When Ralph is chosen leader, everyone seems to be surprised by his election.
None of the boys could have found good reason for this; what intelligence had been shown was traceable to Piggy while the most obvious leader was Jack. (Ch. 1)
The conch shell is another example of necessity being the mother of invention. Since there are no adults and the boys have to keep their own order, they need a way to run meetings. If everyone talked at once, they would never get anything done. Enter the conch. The conch has a special symbolism because it makes a powerful sound, and it originally brought the boys together. So the conch is chosen to be passed around at meetings, and only the one holding it can talk.
I’ll give the conch to the next person to speak. He can hold it when he’s speaking.”
“And he won’t be interrupted: Except by me.” (Ch. 2)
Ralph is the one who designates the conch as the talking stick. The necessity of keeping order at the meeting was the mother of the invention of the conch-holding rule. By doing so, Ralph also cemented his power. He was seen as the bringer, keeper, and user of the conch. Its presence as a power-granter at meetings reinforces his importance.
As the boys try to make their way on the island, they will need to invent shelter, fire, watches, hunting, and other necessities. Their survival is based on their inventiveness and creativity. If they do not invent, they do not survive.