What is said to strengthen another's will to continue. Its root is heart — to encourage is to put heart back in.
Old French encoragier, en- (to put into) plus corage (courage), from Latin cor (heart); to put heart back into someone.
To put heart back into someone is not the same as making them fearless: encouragement supplies the courage to act while the fear is still present, not a verdict that the fear was wrong. What is offered is fuel for the next step, never a judgment on the danger.