"As Latter-day Saints, be careful not to view the entire world outside the family as an ugly place. To be sure, we live in a time when corruption is rampant, but so did Enoch. There are also people about us who are good, kind, and decent. In this and other matters, parents need not be unduly afraid of outside influences if the home is a warm, loving refuge for its members. President David O. McKay explained: "A child has the right to feel that in his home he has a place of refuge, a place of protection from the dangers and evils of the outside world. Family unity and integrity are necessary to supply this need" (Improvement Era, Sept. 1965, p. 757)." - A Parent's Guide
I think I've often felt like in order to protect my children I need to keep them home with me. I think when they are very young this can be beneficial while their testimonies and understanding of who they are is developing. But between the ages of 8 and 12 they should start heading out into the world. And in their teenage years, you need to be willing to let them go and trust them to make good decisions. I absolutely agree with this quote that the depth to which they feel safe and loved in their homes will determine how your children relate to the outside world. I've felt more and more with my oldest child (now 13) that I need to constantly reaffirm to her that I love her, that God loves her, and that she has great worth. That is one of my primary responsibilities right now.