How does Jack show himself to be irresponsible with the fire?

In Chapter 2 of Lord of the Flies Ralph tells the boys that they'll need to build a signal fire if they're going to be rescued. Jack, without being asked, immediately volunteers himself and his hunters/choirboys to head on up the mountain to start a fire. Jack's impetuosity foreshadows how he will later conduct himself. It's also notable, at this relatively early stage in the story, that Jack's fellow choristers are willing to follow him rather than Ralph. The battle lines of a deadly future power struggle are already being drawn.
Jack has now arrogated to himself and his group the responsibility of tending the fire. But there's nothing selfless about Jack's behavior; he's already thinking ahead. As we see later on with the example of the Castle Rock, Jack has an unerring sense of which locations on the island are the most strategically beneficial for building a power base. But Jack soon gets bored with fire tending duties, finding it much more exciting to lead his tribe to go hunting for beasts in the dense jungle.
While Jack and his gang are off on their pig hunting expedition, the fire goes out. Ralph is understandably furious. He spots a ship on the horizon, a ship that could have rescued the boys from the island. But because the fire's gone out, there's now no chance of that happening. When Jack's tribe triumphantly returns carrying a large pig, they are unrepentant. It's obvious that Jack's priorities are completely different from Ralph's; he's much more concerned with being a tribal leader than with being rescued.
A heated argument ensues in which one of the lenses of Piggy's glasses is broken by Jack. The symbolism of the moment is three-fold. First of all, the breaking of the lens symbolizes the victory of savagery over civilization; second, it shows that Jack's growing in power and confidence––a rule-based order will soon give way to brute force; and third, we now have confirmation that, under Jack's despotic rule––whether of boys or animals––will be much more important than maintaining the signal fire first started by Piggy's glasses.