"Why would Jesus have to go for the whole martyr route anyway? Wouldn't he know that he could be far more effective if he lived on to impart his wisdom to the world?"
"Why would the Holy Spirit kill his own followers for a little white lie? That doesn't sound very 'holy'!"
"Why would God exile us to Hell for eternity over an apple? That's hardly a loving thing to do?"
While each is worthy of an in depth response, they are illustrative of a much broader objection. The objection says that since something would be irrational, evil, or otherwise deeply against the character of God, the whole framework must be wrong.
The Bible must be faulty.
We must have Jesus' identity mixed up.
Somehow, if his existence would create such paradoxes, God himself cannot exist.
The move from "The whole framework must be wrong" to the others isn't a logically valid jump. Our understanding could be imperfect, and certain aspects could be wrong, while most of our beliefs could still be true and proper. However the real problem appears before you even get to that jump. It is a deep-seated misunderstanding of the purpose of the Church and the character of God.
Perhaps presupposing materialism, the cynic subconsciously assumes that a perfect deity would have no more concern for the fate of human souls than a human who doesn't believe in those souls to begin with. Presupposing their own moral and legal codes, they try to define Sin according to its affects on others instead of its offensively rebellious nature against God. Not aware of concepts such as holiness (which means being purely and completely set apart for God), they conflate them with ideas such as Justice. Assuming that Jesus was nothing more than a human teacher, they argue that his crucifixion was a failure. Assuming that religions should be about Social work, they are baffled by the Great Commission and argue that churches aren't doing their job. The list continues endlessly.
Sceptics, the vast majority of arguments in this vein attack straw men. The corollary of insisting that we're making a positive assertion and have a burden of proof is that you really can't decide what we're expected to prove! Christians themselves do not perfectly understand God's character or intent, and having been a Christian, even a faithful attendee of Sunday school classes, doesn't make you immune to such a mistake. Just as you would not demand a Muslim defend the eightfold path of Buddhism or a Jew Christianity, have the decency to let people present the arguments and evidence for their God instead of your caricature of him.
Apologists, feel free to tell a cynic that they have indeed disproven the existence of the God they have in their heads, but that is not God. The God they cannot believe in is one that you cannot believe in either! It was a man-made construction, an idealised human blown up with a bicycle pump. You have the true Gospel, you know the God of Heaven or the God who resides in your heart. Be bold in sharing that good news.