A hero is usually tasked with a conquest, he or she have two options; to refuse or accept the call. If he or she refuses the call, there won't be much to the story. Half of the story might be about how unlikely the hero is to accept the call.
The Lion King
In the Lion King, Simba, Mufasa's son, refuses to return the Pride Rock after Scar convinces Simba that he killed his father. After Nala finds Simba living with Timon and Pumbaa, she expects Simba to come back to Pride rock with her to fix the problems that Scar caused. Simba refused at first. But after Rafiki makes Simba see that his destiny can not be changed he returns and fixes the problems that Scar has caused.
Mulan
In Mulan, before her father leaves to fight The Huns, Mulan begs him not go. Mulan fears that her father is weak and will get hurt or even worse, killed. After deciding to leave that night to take his place, Mulan gives back her hair piece that her father gave her. Mulan dressed in her father's armor, cut her hair and took off to training camp to learn to fight in place of her father.