In my opinion a calm, reasonable, and practical approach is best. The old adage, less is more.. I.E. "This is my decision." "Yes, I have thought about it and I have found it reasonable to err on the side of caution." ETC.
I have no children. But if I did my explanation would be, "No - I do not believe our community will become infested with brain-sucking Zombies. No - I do not believe car-jacking-terrorists-selling-crack live next door and shop at our grocery store. I just think that owning and carrying a gun is just one simple move I can make to further protect our family in the event of an emergency, should that emergency ever take place."
Fear-based explanations followed by statistics and speculative "facts" tend to ruffle people's feathers. Honestly, I believe that for many if not most of us, owning/carrying a firearm is in a sense NO BIG DEAL. When it comes to others, present it as such and leave it as such.
Only my own opinion.