The easiest way to define atheism is basically that we don't believe that gods exist. This definition applies to all gods especially the most popular of them all Yahweh. A theist tends to disagree with atheists in that they believe in the god of their choice, and in most cases submit themselves to this god and worship him. Besides the fact that gods have never been proven to exist nor have made their existence known objectively; the theists claim that their subjective experiences of gods are sufficient evidence of his/her/or their existence. For simplicity's sake I will only refer to the Christian God for the rest of this post.
It's ironic that according to theists the only way that you can come to a knowledge of the existence of God is through giving up your basic logic and reasoning skills in favor of faith. It is basically an open admission that God cannot be known he can only be felt and perceived through a sixth sense called spirituality.
And without faith it is impossible to please God, because anyone who comes to him must believe that he exists Hebrews 11:6
Faith is like trust without evidence. Hence the term "leap of faith," you take risks without really being sure of the outcome, but hoping that your beliefs about that desired outcome were correct. Faith asks you to put it all on the line and trust in God despite what any evidence to the contrary may lead you to believe.
5Trust in the Lord with all your heart and lean not on your own understanding;6in all your ways submit to him,and he will make your paths straight. Proverbs 3:5-6
The biggest obstacle between atheism and theism is that an atheist requires evidence before making any life commitments. Most atheists are of an analytical nature we like to solve puzzles and almost universally share a love for the sciences. We like taking things apart and trying to figure out what makes them work. Most of us are naturalist in that we believe that most things in this world including the world and the universe itself are best explained naturally we do not throw in the towel when we come across a mystery that we can't solve. Atheists for the most part have a deep desire to learn and a need to know what can be known about the world we live in.
Aside from the fact that God seems to be hiding from mankind or that his intervention (miracles) in human affairs are nonexistent, another reason we can't believe in God is that we don't believe in so called divine revelation as a means of obtaining knowledge or ascertaining truth. In the case of Judaism, Christianity, and finally Islam we don't accept their so called holy texts namely the Tanakh, New Testament, and the Koran as revelations from their respective deities.
All scriptures are the products of men and not gods
The fact that the Bible is self contradictory and riddled with errors about science and history is a testament against it being a revelation from an omnipotent, omniscient, all knowing God. But Christians have found a solution for this very big and obvious problem. They have modified how they interpret the Bible. If it makes sense then it is taken literally, if it doesn't make sense then it was meant to be taken allegorically, and if it is really absurd then it was a parable with a deeper more spiritual meaning not to be taken literally. There is also the art of cherry picking in which a theist can mix and match verses from the scriptures usually quoted out of context to make a certain doctrine or belief seem more coherent and supported by the scriptures themselves.
Through the art of cherry picking man has found justification for some of the worlds most horrible atrocities. The Bible through cherry picking gave Hitler justification for exterminating the Jews, gave the American South justification for enslaving the African man, gave others the right to treat women like second class citizens and was used by the church fathers as a reason to despise women (misogyny). Because of the Bible and mans interpretations of it so called heretics, witches, devil worshipers were all murdered in cold blood. Christian history is inundated in an ocean of innocent blood. Today's Christians persecute and ostracize others who don't hold their beliefs and make atheists feel like they are not upstanding members of society. They wrongly accuse us of being immoral, vile, evil, etc. What justification do they have for all of these false accusations? The Bible!
You adulterous people, don't you know that friendship with the world means enmity against God? Therefore, anyone who chooses to be a friend of the world becomes an enemy of God. James 4:4
According to the scriptures if you are not a believer and don't accept the gospel as the word of God you are then an enemy of God. The Bible states that the only way you can find reconciliation is through accepting the death and resurrection of Christ by faith.
For if, while we were God's enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life! Romans 5:10
The first problem an atheist may have with this is that there is no evidence for the existence of Yahweh, Jehovah, God whatever you want to call him. Secondly the evidence for Christ fares no better in secular history than God's. If we are to accept that the biblical God exists on faith then also on faith we must give all the other thousands of gods that man has created for himself the benefit of the doubt. Some of those gods threaten some horrible punishments in the afterlife if we don't believe in them now. So this brings up another dilemma: which god should we believe in and how do we determine the truth of his existence?
Atheists can't believe from a logical standpoint in the existence of gods because in our view all gods were created equal! Just as there is no evidence for the existence of Baal, Bacchus, Ani, etc. there is no evidence for Yahweh, Allah, Jehova or whatever you want to call him.
I think that philosophy when applied to religious beliefs is one of the main causes for all the confusion regarding terminology and classification of what we all believe or don't believe. In fact philosophy is called apologetics in Christianity because they misapply philosophical principles to somehow try to justify the incoherence of their beliefs. No one but philosophers waste time pondering the attributes of God, the possibility of his existence outside of space and time, etc. All ridiculous things to ponder without any evidence of them even being real.
Note: All biblical verses are taken from the New International Version of the scriptures.