"I'm fiercely independent, but I'm also terrified of being alone."
For one, I think that it means that though we all want to be independent and "grown up," but everyone has this part of them that's a little child, just lost out there, too shy and too scared of the immensity of the world. Now, if you are a teen (like me!) and you think, "Oh. I need to be cool. I need to act like I don't need any help from anyone," well, you know that inside, buried deep, deep, deep, deep, deep, deep, even deeper, even deeper than that, at the very very center of your heart, that you don't want to be alone. You want someone to lean on.
No one on this Earth grew up alone. Everyone had someone else - family, friends, even pets. Technology extends that even further to strangers. Imagine if all of that disappeared one day, and that you were the only person left. Isn't that kind of terrifying? The freedom! The joy of being alone! The quietness!
But you'll miss it one day.
Now, back to the not-yet-apocalyptic world. Look around you. You see your sibling playing with something or bugging you? You are not alone. You hear your parents lecturing you, yet again, about some little detail? You are not alone. You smell the cookies that your grandma's baking? You are not alone. You feel your pet walking beside you, the air around it moving from your pet's wagging tail? You are not alone. Though you taste the freedom of independence, you are, and never will be alone. No matter what happens to who, what, where, when, why, and how.
You. Will. Not. Be. Alone.