First, an aside: try not to start several different threads on the same thing when you can! For something like this, you can just edit your previous post, which is only a couple hours old, to add the additional info, rather than start an entirely new thread! (as it is, a mod might end up merging them).
But re: the question:
Okay, generally, a couple of the really important components of a character are: the things that they're afraid of, and the things that they want. These can be really obvious things, like "I want treasure" or "I'm afraid of snakes," but they can also be less obvious things, like "I'm afraid of responsibility" or "I want to prove I can be brave." Characters themselves don't always know these things (there are plenty of real people who are afraid of commitment without realising it, for instance) but it's good for you, the creator, to know these things about them.
A lot of times, really important moments in the story are going to reveal these things, because those are the things that drive your character's decisions. A character does something to avoid a thing he's afraid of, or to try to get a thing he wants. The most interesting decisions come when two of these come into conflict. So if you have a character who wants to help people, but is afraid of snakes, and she suddenly sees someone being attacked by a snake, what does she do? Which is more important to her, her desire to avoid snakes, or her desire to help? That tells you a LOT about the character and where their priorities are.
So when you're looking at a character and you need him to be pushed towards something he wouldn't normally do, you can use a lot of these principles. Can something about that decision play into what the character wants? Can something about that decision play into the character's desire to avoid the thing they're afraid of?
A character is afraid of being useless, so even though this quest looks hard he's more afraid of sitting it out and being unable to help. Another character has always wanted to do something important, so even though her life is comfortable she's willing to risk everything for the chance to make a real difference. One character is terrified of stepping into the role that's being asked of him, but it's the only way for him to be close to his closest friend, so he takes the job because he wants nothing more than to stay close to the people he loves. Another character doesn't want adventure, but she's much more afraid of everyone else thinking she's a coward, so she accepts the quest.
"Fear of losing a loved one" is just a very specific use of this -- it's easy, because an audience can assume "he probably wants to rescue his loved one" and you don't have to do the work to establish the character and why he's willing to make the decision. But there are a million other ways to motivate someone, depending on what matters to them, and decisions like this are a great place to reveal what matters most.
