Why do Ralph and Jack decide to go find the beast?
There had been much uncertainty and speculation about the existence of a beast on the island. Ralph had called a meeting to clear things up and it was at this point that Jack brought up the subject. He especially blamed the littluns for their repeated references to the beast stating that:
"You littluns started all this, with the fear talk. Beasts! Where from?"
One of the liitluns claimed that the beast came from the sea and another, Phil, claimed to have heard and seen the beast during the night, but it was soon established that it was Simon who he saw. It was clear, however, that the boys were fearful of this unknown entity and that this fear had in some way led to dissent amongst the boys. Jack promised to hunt down the beast and kill it.
The twins, Sam and Eric, later claimed to have actually heard and seen the beast whilst tending the fire on the mountain. They informed Ralph and a meeting was called. At the meeting Eric said:
"We’ve seen the beast with our own eyes. No—we weren’t asleep—"
Further testimony by the boys was so commanding that they could not but be believed. It was at this point that Jack insisted that they hunt for the beast. His insistence persuaded Ralph to accompany him. Finding the beast would end all speculation and killing it would stop all fear. This was essential to ensure security on the island and probably put an end to dissent.
It is ironic, though, that what Sam and Eric had actually seen and heard was the body of a dead parachutist who had landed on the island. Further irony also lies in the fact that this would be the last time Ralph and Jack would work as partners in the pursuit of a shared objective.
On one level Ralph and Jack both decide to go and find the beast because they are the eldest, and the unspoken "leaders" on the island since there are no adults and no adult authority. On another level, Jack and Ralph BOTH have to go find the beast because to not want to is to admit fear or a weakness and that they are afraid of "something." This is a power struggle that begins to form between the two and will manifest itself in the two tribes splitting and the boys choosing which camp they want to belong to. They are both trying to assert their courage and demonstrate to the rest of the boys that they are both suitable commanders, protectors, and leaders.