One particularly strange objection I've seen to Christianity, or indeed to religion in general, is that it takes away the fear of death. When you're confident that you're going to Heaven after death, you tend not to fear it. In fact, many Christians look forward to Heaven. To many atheists, this is repugnant. In their eyes, life is precious, and death is a bad thing, so to not fear it, and especially to look forward to what comes after it, is horrible.
There are multiple problems with this, the first of which being that no Christian specifically looks forward to death itself. What they look forward to is their resurrection. Think of it this way: A pregnant woman may look forward to her due date. Why? Because she wants to meet her baby, not because the hours of labor that proceed it are particularly enjoyable. In the same way, Christians don't particularly want to die, but why wouldn't we want to go to Heaven when it inevitably happens?
And that's the second problem: It is inevitable. Atheists are not immortal. Atheism adds 0 seconds to a man's life. Even if atheism somehow added a whole century to your life, you would still die eventually. Death is inevitable, and denying that is delusional. So why is it such an awful thing to not fear it, or to have hope beyond it? It's coming for us all, so we might as well live a fruitful life until it comes.
Which brings us to the third problem. If atheists are correct, why even bother to lead a "fruitful" life? After death, nothing matters. You could have lead a long and happy life, or you could have been brutally murdered in your mother's womb (ironically, a policy these same atheists often support), it wouldn't make a difference. You won't remember the good, or the bad. No one will. Atheism is inherently Nihilistic, and frankly, I find that more disturbing than even a false hope of eternal life.
But thankfully, for Christians, the hope isn't even false. There actually is a God, He really did create us, we really did rebel against Him, He really does love us, He really did send His Son to die for us, He really did rise from the dead, and those who believe in Him really will be granted eternal life. And should truth not be our guide? If there really is a hope after this life, why should it matter if atheists find it disturbing that we take it? I guarantee you, no atheist would accept "but if there's no God, life is hopeless" as an argument. Why, then, should anyone accept "if there is a God, death has no sting" as an argument?
Ultimately, the contrast between Christianity and atheism is that Christianity is hopeful and true, whereas atheism is hopeless and false. As Christians, we have reason to preach. Our preaching actually matters, and has eternal consequences. Atheists, by contrast, have no reason to preach. While their preaching does have eternal consequences, they do not believe this. The fact that they not only preach, but actually preach two contradictory messages (hope in a hopeless life), highlights the folly of the atheist worldview. Therefore, turn instead to Jesus, who came that we might have life, and have it to the full (John 10:10).