As an atheist who doesn't want to die, I've heard a lot of arguments as to why I should get over it. Excluding the pearly gates nonsense, they all fall into one of these categories:
You're just changing form
This argument has its roots in new agey concepts that borrow liberally and inaccurately from dead religions and a Dummy's Guide to Buddhism. In various forms it states that what constitutes the essential "me" will continue in the redistributed particles that formerly comprised my body.
The problem: no mechanism for this association has ever been established. The key to "me" is the activity of my consciousness as produced by the chemicals in my brain; the "me" that I'm so attached to ceases to be every time my brain produces enough delta waves. I've heard "vibration" and "energies" as mediators for my consciousness after death, sometimes from the same person, who doesn't seem to understand that energy and vibration are the same thing, though if I point that out, they take it as more evidence for their argument.
If I separate all the plastic parts from all the metal parts in my computer, it is no longer a computer. It can no longer compute. If you've dispensed with the concept of a soul, there's no physical mechanism that could explain the continuation of my consciousness, which, regardless of its ultimate nature, is produced by the balance of chemicals and electricity in my brain, past the end of my body. For me, this is as simple as saying separate letters do not contain the essence of the word once you take them apart. The word is a symbol composed of its letters, scramble the letters, no more word, no more symbol. Scramble my atoms, no more me. The metaphorical sense in which I would continue through my impact on the world is no more me than the impact I have on the world now, and though my impact is impacting away 24/7, it doesn't constitute a consciousness when I'm asleep.
The precise thing I'm attached to is my train of thought and my ability to experience sensory input. There is no other "me" that I care about, because that's the only part of me that cares about anything.
It's part of being human
Yeah, but so was hunting for every meal at one point. It's not a part of being human. "Death" is a term for the cessation of a system that resembles something we refer to as "alive." Since the current laws of our universe dictate that systems degrade as energy becomes unusable through entropy, anything that is "alive" will eventually become "dead." There is no known way around this. Even if all the physical degradation to my body were to cease forever and I were made as indestructible as the element of your choice, all it takes is a passing black hole or a well-placed nuke.
Nothing will last forever, as far as we know. But that's no reason not to try to last a really long time. I think people understand this, so what they're really saying is, "It's part of being human to die around 80, at least in first world countries." That isn't true: it used to be around 40, and once it was closer to 20. So why not 400? Or 10,000,000?
We don't know what death is, so there's no reason to fear it
I heard this a lot in college, since it was Socrates's argument. However, I'm pretty sure I do know what death is, and claims to the contrary are ignorant or delusional.
Death will be nothing, so why be afraid of it?
I find "nothing" very scary. More to the point, any purpose to my life is self-contained, and ceases with my life.
You should join something bigger than yourself, to give your life meaning so you won't feel bad about dying
Bullshit. These are the people who disagree with my statement above about purpose being self-contained, yet everyone who says this has a suggestion on hand about me doing something that's very important to them. Just because something is important to a lot of other people doesn't make its purpose "bigger" or important to me. The people it is important to feel better about contributing, but they're doing the same thing I'm doing when I get a drink: feeling better about themselves. I assume they also like being in groups and feeling a sense of belonging. I like several groups of people, but I don't need to feel like I belong. So the extra work groups demand implicitly or explicitly in exchange for that feeling of belonging is just a waste of energy for me.
Furthermore, every time I talk to another person or work an hour at my job or breath air, I'm technically "part of something bigger." The suggestion that if a purpose is "big" enough, or shared by enough people, that it attains some emergent property of being anything besides an idea held in the heads of many different people, is a fallacy not unlike the notion that my being will live on in "vibrations."
And even on the rare occasions I join in the struggle for some abstract social or political issue, it gives me all the warm and fuzzy it's supposed to, but doesn't make me a happier, better person, nor does it extinguish my fear of death.1
You can't enjoy your life if you're afraid of death
This just isn't true. I enjoy my life all the time. I enjoy it more than most people I know, probably because I want to fill my life with awesomeness before I die. Being afraid of dying isn't the same as being afraid of living, which is what most people suffer from. In fact, if you logically narrow down your fear to the fear of death in a strictly physical universe, all the rules and social anxiety and childhood issues and whatever else people worry about just go away, rendered pointless in the face of life and experience being the sole achievements of the "me" that I want to keep living and experiencing.
You're a selfish bastard
Yes. I am solipsistic in the extreme, but so are you, I'm just honest about it. I don't delude myself with notions of exterior judgement meaning anything more than my judgement.
You have no moral center or guidance, what's to stop you from killing people?
Upbringing and empathy. The great thing about empathy is that there are no qualifiers. It just says, "Don't make other people feel bad, because that will automatically make you feel bad." It doesn't say, "Don't make other people feel bad unless they're black," or "Don't hurt Christian people," or "Don't kill people in the gang." It also doesn't tell you to be nice to people in a particular way, or give you an excuse to say, "Well, I was acting properly, they shouldn't be upset."
I also have this huge system of people around me that makes the consequences outweigh any possible benefits, unless it was a strictly them or me circumstance.
Haven't you heard of "dying well?"
Yeah, but I don't buy it. That inevitably means dying for somebody else's interpretation of well or good, since it won't matter to me. All philosophical drivel to the contrary is wordplay from people who think they are Right About Something and are content with being Right, and their curiosity gives way to satisfaction. Since I don't believe in being Right, I'm infinitely curious about finding out more, so I don't believe my life will ever be "finished" in some sense other than it abruptly ending.
1 Exception: World of Warcraft cures all existential fear. And that's definitely being part of something bigger.