Joseph F. Smith lost his father at age 5 and his mother when he was only 14. He had an extreme love for his family, and struggled with the death of both parents. He took his responsibility as brother very seriously, and was willing to fight any threat to his family. Joseph F. had a fiery temper, which was acknowledged by all those who knew him in his early life. It got him in trouble but also may have been an important trigger in his life.
One day in a school class, the school master threatened to either whip or use a cane on Joseph F. Smith's sister. Joseph F. Smith objected to the whipping of his sister. We do not know exactly what was said, to the teacher but the idea was "don't do it" maybe even added a threat. The school master, instead, came after Joseph F. to beat him instead. Joseph F. was not a small teenager, and instead of taking the thrashing, Joseph F. turned the thrashing back onto the teacher. This ended in the expelling of Jospeh F. from the school.
One of the histories said "the brethren felt that perhaps his energy should be channeled in another direction." So, he was called on a mission at the tender age of 15. Joseph F. was called to the Sandwich Islands, also known as Hawaii.
Reference:
"The Presidents of the Church" by Truman G. Madsen