I'm late answering this but...

It's important to step back from the word "pardon" in this case. Many presidential pardons today are issued when there is a perceived injustice or when someone's good deeds might outweigh the perception of their punishment. And of course there's controversial pardons that seem to reward loyalty. But in the case of Brigham Young and the Mormons, the pardon was offered on condition of submitting themselves to the laws and governance of the United States. While it was first written in April 1858, it was kept secret by Buchanan and not executed until June 1858 by the peace commission assigned to negotiate with the Mormons. Even then, it was a strange "pardon."

First and foremost, it does not mention Brigham Young by name; the pardon was offered to all Mormons considered to be in rebellion. Buchanan's April 1858 proclamation spends most of its length chastising the Mormons, accusing them of treason and a litany of other crimes and misbehavior. Only at the end does it mention a pardon, offered only on condition of submission "to the laws" and a promise that for those who continue in rebellion, there will be no leniency. The offer was made at the tail end of the Utah War, when it looked as though peace might be achieved. It was Buchanan's carrot on the stick to the Mormons, after he had bungled much of the war and the negotiations. Remember that, while the causes of the war are multifaceted, it did not help that Buchanan appointed a territorial governor to replace Young and promptly neglected to tell Young. Buchanan later acknowledged his mistake and sometimes came across in letters as if he were saying, "Yeah, my bad, sorry about that."

Throughout the cold Utah War, negotiations went on to bring an end to the conflict. Thomas Kane, a longtime friend of the Mormons, worked with Buchanan, as did the Mormon territorial delegate to Congress, John M. Bernhisel. A peace commission was assigned and Utah's new governor, Alfred Cummings, was also kept abreast of things. Buchanan likely acted alone when crafting his proclamation. He wanted an end to the war and as things progressed positively, he informed Congress that Utah was no longer in rebellion. Reports said that laughter broke out in Congress when they got his message. Still, Buchanan was largely right that tensions had thawed and he did succeed in ending the war...that he helped to cause.

The Mormon pardon was controversial at the time. Brigham Young was viewed as a zealot and a tyrant outside of Utah. Soldiers sent to Utah mocked the pardon as something that forgave past treason in exchange for the promise of future good behavior that they were certain would not happen. Outsiders who came to Utah often believed that people in the East did not understand the depth of Mormon loyalty to their faith and disloyalty to the United States. They felt (correctly) that Utahns would continue to follow their leaders and not the government. Mormons fled the states in 1846 and settled in what was then Mexican territory. (I'm of the opinion that Mormons knew that they wouldn't be free of the United States for long; they were aware of the Mexican–American War and its likely outcome and consequences.) While Mormons felt allegiance to the United States as their heritage, they felt no allegiance to its leaders or government. What's more, most Mormon converts came from Europe, where they sailed to New York or New Orleans and crossed the plains to Utah; they had little reason to care about the US government. LDS leaders often railed against government officials and non-Mormons invading Utah. But the pardon was offered and when all was said and done, it was easy for most Americans to forget about Utah and the Mormons as divisions between North and South boiled over.

In summary, Buchanan wasn't afraid of Young or awed by him so much as he was embarrassed by the Utah War and sought a quick resolution. He offered a pardon to all Mormons and it led, in part, to the end of the Utah War.

Further reading: Bill MacKinnon is the authority on the Utah War and no one else even comes close. His two-volume semi-documentary history, "At Sword's Point" is the standard and he's written dozens of articles on the war and its aftermath.