I've figured it out.

I used to think that death was something new. Something I've never faced before. I didn't know what it was like, and I was afraid of it. After all, what could being dead be like? Do heaven and hell exist? Is there some other place that people go when they die? Is it an eternity of blackness? Does consciousness just end when you die?

All these questions left me fearful of being dead, and the fear of being dead led me away from accepting myself as temporary. I put thoughts of a finite life out of my head, and only came back to them occasionally, where I would cut myself short of a conclusion because I was missing a piece of the puzzle.

I failed to realize that I had been dead for an eternity already. How long had gone by without me existing? And all of that time went by as if it were nothing at all. The creation of the earth, the beginnings of life, and the age of the dinosaurs, they all went by without me, and it felt like no time at all. That all went by without me even catching a glimpse of consciousness, and then one day I awoke to this world. I remember being in kindergarten, and I was astonished when my teacher said that it was the year 1998. I could hardly believe that so much time had gone by. It seems like unconsciousness is exactly what they say it is.

"There was a time when we were not: this gives us no concern -- why then should it trouble us that a time will come when we shall cease to be?" - William Hazlitt

"Would you not think him an utter fool who wept because he was not alive a thousand years ago? And is he not just as much of a fool who weeps because he will not be alive a thousand years from now? It is all the same; you will not be, and you were not." - Seneca

This is where I find comfort in death. It is not something new. It's going back  to the way things were before. I know what being dead, or rather, not existing will be like. I was dead until I was alive, and I will be dead once more. Death isn't something to be afraid of anymore. It is simply an ending to the story of my life. I accept it, and I find comfort in it.

I am all of a sudden perfectly happy with this life, and the nothingness that will come after. Every breath tastes sweet, and even the feeling of my fingers against each other is pleasant. How wonderful it is to be alive and breathing. To be seeing, hearing and feeling. I'll know everything there is for me to know and go without any fear or regret. I've been there before; I've spent an eternity in non-existence, and when I think about it, spending another doesn't seem all that bad.
It seems like it's just a part of life.