We discover later on in the story that it was the evil Captain Jaggery who killed Mr. Hollybrass. The deadly deed took place during—appropriately enough—a violent storm, when Jaggery plunged a knife into his first mate's back. This was out of revenge for Hollybrass daring to question Jaggery's crazy decision to sail the good ship Seahawk straight into the eye of a raging hurricane.

As well as being a violent, blood-crazed maniac, Jaggery is also a total coward who's not prepared to take responsibility for his actions. He therefore has no hesitation in setting up a patsy to take the blame for his wicked crime. That's where Charlotte Doyle enters the picture. Jaggery has been longing to rid himself of what he regards as an important trouble-maker for quite some time and sees this as a great opportunity to do just that. So he shamelessly puts the blame on Charlotte for Hollybrass's death.

In an outrageous miscarriage of justice, Charlotte is tried for the murder of Mr. Hollybrass, convicted, and sentenced to hang. Thankfully, Zachariah, whom Charlotte thought was dead, helps her to escape from the brig, where she's been holed up awaiting her execution. The stage is then set for the truth of what really happened to Mr. Hollybrass to emerge.

The Seahawk has sailed into the eye of a hurricane. For just a little while, calm descends upon the ship as the crew works frantically to prepare for the next onslaught. But then a surprise. A fallen sail is drawn back, and beneath it lies first mate Mr. Hollybrass, dead with Charlotte Doyle's knife stuck in his back and her handkerchief clutched in his hand (chapter 15).

Charlotte seems to be the most likely culprit. Even the crew members are suspicious. Charlotte knows that she is innocent, but she has her own suspicions, for she had caught a glimpse of Zachariah...Zachariah, whom she thought was dead and buried at sea. Yet she saw him in the midst of the storm. Could he have killed Mr. Hollybrass?

Captain Jaggery accuses Charlotte, for he has hated her from the time she lashed out against his treatment of Zachariah and struck him. Indeed, the situation looks bleak for Charlotte, who is tried and condemned. Even though Zachariah has convinced her of his innocence, they must quickly discover the real culprit before Charlotte is hung. As they discuss the situation, a light suddenly dawns on both of them. They had both seen Captain Jaggery and Mr. Hollybrass arguing during the storm. In fact, Zachariah says, “I heard Hollybrass accuse the captain of deliberately taking the Seahawk into the storm.” “Jaggery was enraged,” he continues. “I thought he was about to strike the man” (chapter 19).

Indeed, Captain Jaggery, so filled with pride and anger, could not bear to be accused of or even questioned about anything. He was furious that his first mate had dared to object to one of his orders. After all, he was the master of the ship, and he had once told his crew,

If you give me less—one finger less—than the particulars of the articles you have signed, I shall take my due...No, we shall have no democracy here...There's but one master on this ship, and that is me (Chapter 3).

The captain demands complete obedience, even, perhaps especially, from his first mate. Anyone who fails in that will feel the captain's wrath, and Mr. Hollybrass certainly does.

For indeed, it is Captain Jaggery, in his pride and anger, in his arrogance and fury, and perhaps even in his fear (for anyone who demands such unquestioning obedience is clearly afraid of not getting it), who murders Mr. Hollybrass. He finally confesses as much to Charlotte, admitting,

He threatened me...And in the midst of that storm. It was intolerable (chapter 21).

What Mr. Hollybrass had really threatened was Captain Jaggery's ego, and it cost the first mate his life.

The answer to your question is in chapter 21. In that chapter, Captain Jaggery confesses to killing Mr. Hollybrass.

According to Captain Jaggery, he killed My. Hollybrass after the latter threatened him in the midst of the storm. The captain excuses his actions by arguing that Mr. Hollybrass's behavior was intolerable to him.

Recall that in chapter 15, Charlotte's handkerchief was found in the dead man's grasp. Accordingly, Charlotte's dirk was also stuck in Mr. Holybrass's back. Not long after "discovering" Mr. Hollybrass' body, Captain Jaggery blames Charlotte for the sailor's murder.

In chapter 17, Charlotte discovers that Zechariah is still alive. For his part, Zechariah can't believe that Charlotte killed Mr. Hollybrass. Unfortunately for Charlotte, Captain Jaggery sentences her to death by hanging from the yardarm. You can read about this in chapter 18.

It isn't until chapter 21 that Captain Jaggery confesses to Charlotte that he was the one who killed Mr. Hollybrass. Captain Jaggery also says that he blamed Charlotte for the sailor's death as a matter of convenience. After all, she is an outsider.

So, Captain Jaggery killed Mr. Hollybrass because the latter challenged his authority during the storm. Accordingly, the captain gave certain logistical orders during the storm that Mr. Hollybrass disagreed with. The sailor then accused the captain of taking the Seahawk directly into the storm. For his part, Captain Jaggery took Mr. Hollybrass's attitude as insubordination. This is why he killed Mr. Hollybrass.

It was Captain Jaggery who killed Mr. Hollybrass, his first mate and most loyal crew member, over an argument concerning sailing through a storm.

When the hurricane was about to hit, Charlotte heard Jaggery and Hollybrass arguing heavily over what to do. CPT Jaggery wanted to sail through because it would look good in his book, and would enhance his already blown-up ego. Hollybrass thought that this was a stupid decision. The problem is that the issue escalated to the point of murder. This was also a great opportunity to get Charlotte involved, since Captain Jaggery really began to detest her, so this is exactly what he did.