1) Reasons for not believing presented in a video by healthyaddict: http://www.youtube.com/watch?v=TUYCiSGdIpk&feature=channel
2) 80 problems atheists commonly find with the Christian god from a Wadsworth: http://richarddawkins.net/articles/5481#482570
There are three major fallacies used in arguments for a god's existence:
1)Argument from ignorance- This is to put a god or miracle in a gap of your knowledge in order to explain a phenomena. A theory should not be based on lack of evidence because theories by definition are based on a lot of testable data. "I do not know how this occurred;therefore, it was a miracle "
2)Fallacy of Composition- This is attributing qualities of the parts to the whole unjustifiably. "Every painting has a painter; therefore, the universe has a creator."
3) Special pleading-emphasizing favorable details and ignoring that unfavorable details. "Look at how times prayer worked, and ignore the misses." Also, it is creating special rules that make ones hypothesis possible. "Everything has a cause, except god."
Premise 1: Everything has a cause
Premise 2: The universe had to start sometime (a big bang)
Premise 3: The only thing that could have been the first cause is something that is outside the chain of cause and effect
Premise 4: God is outside cause and effect
Conclusion: God created the universe
Problem 1: It would be a fallacy of composition to say everything has a cause. For instance, most events, especially quantum events, have a random component.
Problem 2: Even if the universe started with a big bang, it does not necessarily concludes that was the real beginning. There could have been a multi-verse.
Problem 3: There is no evidence that the universe cannot exist on its own. If there is no god, it could exist on its own. Also, imagine a scientist created a mini-big bang in a laboratory like the scientists at CERN are doing. Our universe could just a tiny one inside a larger universe necessitated on the scientist experiment. Because time is just the order in which events occur (our thoughts not being excluded from that), all of history could be contained in one minute of this larger universe's time. This scientist is not god, but our universe is necessitated by an experiment in a larger universe which is not necessitated on anything else.
Problem 4: It is special pleading to make god excluded from cause and effect, an earlier premise.
Problem 5: It is multiplying variables beyond necessity to create this new entity in order to explain what is in this universe. It is even necessary to add powers and supernatural characteristics like a floating will that is not sustained by physical processes like human wills or being able to affect the physical world without being physical. Occam's Razor makes god unnecessary to explain the universe. It is very dubious to add all these variables that it makes a god more and more unlikely for all the powers that would have to be attributed to a god to make it able to even know what it did.
2) Teleological argument:
Premise 1: The Universe has order. The particles move. Laws govern that movement. Evolution occurs. Earth is in the ideal place for life. The universe is fined tuned for life. (These are various versions of the first premise.)
Premise 2: Everything in the universe is governed by these laws.
Premise 3: These laws must be sustained by something outside of it or these laws would not exist.
Premise 4: Only a god exists outside the laws of the universe and has the powers to manipulate them.
Conclusion 1: God sustains the laws of the universe.
Problem 1: premise 3 and 4 both assume things that are unprovable; therefore, they can be eliminated.
Problem 2: Saying that the universe is finely tuned assumes a n conscious entity actively tuned it. This assumes complexity must come from more complexity, which is not verified. There is evidence that unintelligent, simple things can produce complex results. For instance, most living things are mostly four elements. Computers work on a binary system and do not literally understand math yet can do it. It is not necessary to have intelligence or to be complex to create more complex things. For instance, most things are made of parts. A single zygote divides and builds a human body.
Problem 3: Evolution has led to more complex lifeforms in a slow process. Evolutionary Neglect is the negative traits that get passed down because there is not enough pressure from natural selection to remove them. For instance, the human heart has the some of the same weakness as a fish heart. There are genetic diseases like aggressive childhood leukemia. For more on this subject: http://www.youtube.com/watch?v=p_nqySMvkcw
3) Argument for a deity of divine justice
Premise 1: People do good things and bad things.
Premise 2: There is a justice in the universe that causes bad things to happen to bad people and good things to happen to good people.
Premise 3: There is a previous life and after life system.
Premise 4: Only a deity could bring this kind of justice and order.
Conclusion 1: All bad things that happen to people are deserved because of this justice.
Conclusion 2: There is a deity from whom all justice flows.
Conclusion 3: People who suffer without committing evil deeds in this life are being punished for past lives or original sin.
Conclusion 4: People, who do not get punished during this life, will be punished in the next.
Note: This is more of theology than an argument for a deity. But it is important to note that this argument is a blend of the argument for morality and teleological argument.
Problem 1: Premise 2 is too strong. There is a tendency for bad things to happen to bad people, but it does not seem absolute.
Problem 2: Without evidence for premise 3, the argument falls apart. There is no conclusive evidence so far for an afterlife, though many claim to have it from near death experiences.
Problem 3: Premise 4 has the problem as the teleological argument had.
Problem 4: It become difficult to tell the difference between someone doing an evil deed and someone being punished indirectly for their bad karma.
Problem 5: This also leads to interpretation to why things happen in a supernatural sense rather than a natural sense (i.e. as science would describe it).
I know i need to edit. It is still in its rough stages.
As you can tell, I am not yet done, but bare with me. I will be after a short break. Other things to cover: more deductive arguments, predestination, impossible qualities of god, inductive arguments against god, where is the evidence?, and arguments against belief. The structure against religion can be argued somewhere else in some other post.