Many questions toward atheists are equally unanswered for in Christianity. While I believe that God Himself answers them all, Christianity doesn't and somehow manages to sidestep the reality of such questions, or even worse, ostracises those within for asking them. I have first-hand experience with this.
A few typical questions asked of atheists by Christians are (and I've borrowed some from Suneal's post 'Openness Theology has Tea with Atheism'):
1) How do you place one value over and above another without the constant of God to arbitrate?
2) Why would you feel any inclination to defend or purpose or initiate anything? What would be the point?
3) What is the purpose of life to you? Why bother with anything, trying anything, most especially attempting civility and altruism? What benefit are these?
4) From where are derived such realities as justice, mercy, art, music, thought, charity, love, effort, ad nauseum things that Christians attribute to God's character...?
I could posit myriad *reasonable* (non-Christian-faith-based) responses to these questions, and I believe in the ultimate/eternal/everlasting Lordship and salvation of Christ. The point is that these questions alone will never be sufficient for pointing out error; I'm not even sure they *could* point out error.
I believe that all are created in the image of God; therefore, all are capable of acting in accordance with His image (at least some of the time) regardless of whether or not they choose to acknowledge Him. Asking an atheist to account for morality as if to corner him toward God misses his point at best, and misses God's point at worst.
I think there are definitely huge problems with atheism, but asking existential questions that the whole of humanity has and continues to struggle with camouflages the real problem.
Christians want to know why atheists can't see God. Christ told His disciples that the world would know God because of how the disciples loved one another. Since there is a greater love vacuum in the church than elsewhere (where we wouldn't *expect* to see it), how could *anybody* recognise God in the world?
Did Christ say that the world would know Him through the love of His disciples toward one another and if they don't love one another He would perform a great miracle to convince everyone anyway, so don't worry about it? Did He only mean that IF His disciples loved one another then obviously the world would be forced to recognise the One who IS that love? Or, did He mean this as He said it? That the world WOULD know Him BECAUSE of the love His disciples had for one another?
I think the questions atheism poses directly correlate to the lack of love in the church, which is why as we see an increasing absense of love amongst believers, we see an increasing frustration from those outside. They are crying out for what their souls need, and they cannot get it because we're supposed to be giving it to them, and in our own lack, we're not. We're not BEING the love that GOD IS in us!!! We have taken His 'talent' and buried it-- deep-- so deep that nobody can see it.
So essentially, unbelief is a *believer's* problem. If my children or my friends don't think they are loved, it is my neglect and lack of willingness to extend Christ's unconditional love through me toward them that has brought this about, even if I can point at reasons for my actions, even if I can point at how they weren't willing to receive it, even if... whatever; I'm judging THEM as though I were God, and not at all living the love of Christ, but rather living the judgment of the forbidden tree from which I think I can sustain myself, but which instead of feeding me is actually the source of my starvation, and theirs. Ultimately, I have to be willing to give love at all cost and unconditionally, and until I do, my questions or calls to account belong aimed at me.
The community of believers known as and who is the Body of Christ Himself has the much greater calling to truly and pragmatically LOVE than to bring unbelief to account, especially having contributed so much clanging to the 'cause.'
So let's get to it.
There is no sense in screaming in someone's face while slapping them on the cheeks, "WHY CAN'T YOU SEE HOW LOVED YOU ARE???!!!"