What are the most common arguments Christians use and their counters?
It's hard to choose just one. Traditional arguments such as the argument from creating the universe (metaphysical argument) and the argument from the justification of infinite properties (it takes goodness to create humanity, or it takes omnipotence to create the universe) are very common.
Common arguments against are that there is no evidence of a physical God, that the Big Bang could have been an expansion from another universe and universes are timeless and eternal and natural, that Biblical accounts are not accurate about real history that scientists have studied, that life evolved through gradually more intelligent mutations, and that the process of evolution is cruel and therefore not ruled by a benevolent over-mind.
Another more traditional argument against religion is from the existence of evil, and religious people counter with the existence of Satan, which doesn't seem like a religious argument at all, but something fictitious.
Religion could exist but it's a coincidence, versus a bigger story that is somewhat disappointing. It's as if science is defending religion, but not human mental limitations. God might be old news, and science might be the new religion. But Babel is still in play.
Small details are more important than the tautologies of religious and scientific institutions. We're supposed to love our brother, but we're not supposed to be idiots. Science is king, but has its limitations. Religion mops the floor, sometimes literally. But good ideas take off, and are fossilized beyond the imagination of man.
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