Why did this new leader decide to lead his people west? (John Smith if Jesus Christ of Latter Day Saints)

The general consensus behind why the Mormons headed West was that the West was seen as a place where they could practice their new religion without interference, harassment, or legal restrictions.

Since the founding of The Church of Jesus Christ of Latter-day Saints in 1830, its members have been persecuted because of their religious beliefs, and also because of the actions of its leaders. Relations between Mormons and residents of other nearby Christian communities were often tense. All this forced the Mormons to move from one place to another.

In 1833, there was a conflict between the Mormons and their neighbors in Missouri, which became known as the 1838 Mormon War. The conflict lasted from August 6, 1838 to November 1, 1838. Its victims were 22 people. The state of Missouri accused the Mormons of fomenting conflict and forced them to sell all of their land.

After that, a large group of Mormons traveled to Illinois, where they founded the city of Nauvoo. Joseph Smith became the mayor of this city. He was later arrested and killed along with his brother Hyrum while trying to escape in 1844 in the city of Carthage, Illinois. Due to threats from militia leaders, Mormons were forced to leave. After Smith's death, Brigham Young and John Smith became the new Mormon leaders. Under their leadership, members of The Church of Jesus Christ of Latter-day Saints left Illinois and began to relocate to the West.