Many of these are too off-topic and not so much logical objections as they are personal projections. But in the interest of being thorough, and since these come up frequently enough, I decided to include them here.
Could Jesus have sinned?
If we accept that Jesus is God, then to ask if he could have sinned would be like asking someone, "don't think of a black cat." Since sin is the opposite of God's will. Jesus does talk about doing the will of his Father in the Gospels, and at Gethsemane he asks if possible to not go through his impending doom, sort of as wishful thinking (Matt. 26:39), since he's well-aware the entire time that this has to happen (Mark 8:31-33, 9:31; Matt. 26:53).
Does God want unbelievers damned (justice) or saved our of love (mercy)?
This would almost be a philosophical joke if it wasn't so absurd and devoid of common sense. The argument goes like:
Obviously the condition is that they are turned from their ways and become savable, and one can still love their child even if he went down a wrong path. But you're not going to condone his ways or try to let him get away with serious crimes that harm others.
- Does God love everyone and want them saved?
- Will God damn anyone?
If I have a job that I strongly dislike, I could both hate and like it because of the money it brings. It's simply looking at it from different angles and time-sensitive conditions (e.g. I hate doing some parts of it; love it when it pays my bills). This is essentially the reason why the Lottery and Preface Paradoxes are perfectly valid when they show that it's logical to hold contradictory notions simultaneously.
God is not a stickler (Matt. 12:7), but mercy cannot contradict justice (Matt. 12:20; Luke 18:7-8).
Even if it's objected that it's not that I both hate and love a deadend job that pays my bills, but merely I only like it to a certain degree, or that I don't like it at all, but tolerate or accept it, the fact that two contradictory ideas can be rationally and consciously held at the same time is fully valid such as the Preface and Lottery Paradoxes. This is because they are based on contingents, just like the case with God's justice and salvation due to love.
Why does God need us to worship him?
If someone wants to be admired, even for a genuine talent, we'd call him emotionally unfulfilled. Perhaps unstable. The command for God alone to be worshipped is explained by God Himself in the Old Testament because He's "a jealous God" (Exodus 20:5). This is obviously a euphemism or He would've accepted lip service a little like us. In reality, the meaning is to simply abandon idolatry. And God simply instructs us to worship Him in the sense that we love Him, as well as ourselves - nothing wrong with that.
The question does come up, though. Why the big deal over idolatry? Even if it's a false belief, objectively it may seem a little unusual if your favorite music band demanded that you don't like any other singers. But unlike these other musicians, other gods don't exist, so the kind of people who would make them up have to be lying and cannot have anything good in mind (Rom. 1:21-23; 3 John 1:9-10), hence the penalty against it in the Mosaic Law (specifically since the Canaanite religion practiced child sacrifice). And ultimately, if the all-good Creator of the universe (and everything else) wished to be acknowledged as the sole Creator, I don't think anyone could hold that against Him.
The question of why the Creator can impose His personal preferences (aside from logical laws like the Golden Rule, no theft/murder, etc) can easily be answered by the fact that God knows who and why would truly reject Him (or replace/diminish Him), and it's not an unreasonable request otherwise. Unlike the prohibition of fornication or other (mostly sexually immoral) sins, it would be neither symbolic (of temperance), nor the prevention of injustice to others, and so remains as part of God's personality.
A related observation is the biblical emphasis to "fear" God. Of course, no one would consider fear to be a proper substitute for, let alone more powerful than love. The phrase simply means that the person is afraid of disobeying God and not a different deity - i.e. idolatry (Judges 6:10). So the emphasis is on God, not the fear, which is a practical expression since we all mess up.
If God is completely holy, how could Jesus have a "filthy" human nature?
This I've seen frequently from Muslims, who object to Jesus being God in that he could then be degraded like one of us. But it's a little difficult for me to understand how, if God created everything, this is supposed to somehow degrade him if he came in human form and didn't do anything wrong himself.
For this reason, the Gnostics had Jesus have a non-corporeal illusion of a body. Marcion, for example, edited Luke's Gospel (the only Gospel he accepted) by deleting the first two chapters of Jesus' infancy and had him come down straight from Heaven. The issue is more explicitly stated by a 13th century ascetic, Barlaam. He essentially argued that God could have no contact with an impure world like this, which led him to conclude that revelations and miracles couldn't exist and certainly weren't from God: the natural conclusion from the above logic.
This is why it's important to let go of our human bias and distinguish between what our physical body considers "wrong" (e.g. ugly), in favor of our spiritual mind's. This very spite against fallen nature is what has Paul writing about strength through weakness (2 Cor. 12:7-10) and victory through defeat and foolishness (1 Cor. 1:18-25). One of the Eastern Orthodox hymns has a line that says, "through death he killed death" - victory through defeat (1 Cor. 15:54-57).
What if the Bible was written by Satan?
What if Satan's trap is to make us think we're saved? What if what we think is good (our conscience) is just a trick? It would be strange that he would put so many restrictions and few outlets (such as greed or power). I guess ultimately this is similar to the question of "what if God was evil?" because obviously He wouldn't let Satan tamper with His plan. And if God were evil and He was just fooling us into thinking we were saved...well, what could we do?
How can we truly understand and worship God if He's infinite and we're finite?
It's true that none of us can know the infinity of God. But do I need to know the laws of physics to ride a bike? Am I not allowed to form a general idea that conveys a point by summarizing technical things? Is God a legalist? God's expectations from us are not for us to know how many angels can fit on the head of a pin anyway. Our conscience is with respect to ourselves, and if He gave us a mind capable of understanding, it can be presumed we can understand what He wants well enough. Especially since the ethics are with respect to our knowledge and the physical world (Romans 14).
If God is infinite, how is there "room" for us?
A little strange tangent of a question. But if one understood a little math (Set Theory), one would know that the highest cardinality allows for the existence of lower infinities, hence how a room can have a finite length with an infinite number of midpoints.
How can Jesus be both fully human and fully divine?
This question I feel is usually seriously asked by well-meaning people who don't know much about Christianity in general. Having a human body doesn't need to be an impossibility for God. It's not equating humans with God, because it's just the human nature that's operated. Form and information/function matters: a person is composed of molecules that if rearranged could be ordinary inanimate matter: how then can a person be both living and inanimate?
It's not like saying someone is 100% Irish and 100% Italian. Or 100% robot and 100% human. For some things Jesus was just like us (fear, physical body); for others - unique (being God's Messiah). Just as every one of us is fully human but different, so also Jesus.
Why do I need religion? Why can't I just be spiritual?
Religion is mainly a term used for a common understanding of spirituality. So one can call Buddhism or Confucianism a religion, but for their practitioners it could be just a philosophy. Justin Martyr, a 2nd century Christian writer, talked about finding the one true philosophy, settling on Christianity. Scholars call Christianity in its early days a "cult" non-perjoratively. Originally it was called "the Way" (Acts 9:2).
It's true that there's quite a bit of development in, e.g. the Catholic Church: sacraments, hymns, and many other rites. But again, these are expressions of what's taught. If God had a particular set of rules (e.g. the Mosaic Law), call it whatever you want, but that would be something spiritual. If one has a problem with rules, that's a different story. But regardless of the religion, these are never meant to shackle anybody (Romans 14:5). In fact, Jesus says he came to lift these kinds of obstacles (Matt. 11:28-30). Even the restrictive parts are simply reasonable boundary lines, such as "Do not steal" - I mean I don't mind signs that tell me not to enter a one-way street.
If Jesus is God, are his death/achievements less relevant?
This argument I heard from Reza Aslan who essentially commented on the power of religious narrative by saying, "Sure Jesus rose from the dead. But, so what? He's God." This kind of logic means that now that there are more people in the world who on average live longer that life is less valuable? Jesus needs to not be God for his story and message to be powerful?
Since Jesus took all of these things on faith and didn't actually have the ability to exercise omnipotence as a human as was his choice, I'd say this is a pretty good example of a meaningful sacrifice. Otherwise what do we need to satisfy this all too human bias of being partial to position? Someone powerless no matter what?
Believers saved from what?
This question Christopher Hitchen asked in a slightly different context. Originally he meant "Why can't God forgive without sacrifice?" But I feel another good question brews from this. What exactly are we being saved from by God/Jesus? Our sins? What are they doing to us or anyone?
Of course sins like murder, hate, theft, lying hurt others. But the point is that we are saved from these sins of ours. I suppose it's a euphemism because we're saved from the punishment these sins entail. And since God is in no position to be forced to forgive, this is what's meant.
Should parents "indoctrinate" religion in their kids?
I guess teaching a child about God isn't quite like patriotism or getting them to be a fan of the same sports team as you. But there's nothing wrong in teaching your child what you know best. And nobody considers religion to teach bad values except for the die-hard atheists who go around putting the Bible in the fiction section at bookstores and libraries. If the child grows up unbelieving, that's their business, and the Bible explicitly teaches everyone is ultimately responsible for themselves (Gal. 6:4-5).
Jesus does say not to prevent children from following his ways (Matt. 10:42; 18:10-14). And of course, no one should teach them evil (Matt. 18:6). But he praises the purity and innocence of a child (Matt. 18:1-5). Similarly, God defended Balaam's innocent donkey from his beatings by allowing it to speak and reprove him (Numbers 22:28-34).