Atheists often try to position themselves as neutral rather than admitting they believe God does not exist, but that is not definitionally accurate. The correct term for "a person who claims neither faith nor disbelief in God" is agnostic. (Source: Google for "define:agnostic.") The neutral position is agnosticism as shown in this helpful diagram.
Most atheists I've encountered seem to believe their position is neutral. One atheist I know even defines atheism as "resetting your mind to its default position." Atheists seem to believe that by not having a positive belief in theism they are free and unencumbered by the trappings of "faith" or other beliefs they enjoy portraying as superstition. That isn't true either. This is a category error of conflating supra-natural with superstition.
A more honest way of viewing this is to see atheists as anti-believers who have anti-faith. In absolute value terms, they do have belief and faith! And their arguments typically reveal that in short order. You don't have to spend much time with a self-professed atheist to see their neutrality argument is fallacious. Smart atheists are careful to stay away from the gnostic atheist position, but nearly every self-professed atheist I know will try to reposition the agnostic atheist position as being "free from belief" which is the pure agnostic position.
Some atheists play word games with terms like "hard" or "soft" atheism to try and make a distinction between the radical and outspoken New Atheist evangelists and the less enthusiastic variety that prefers to errantly claim freedom from faith. I've also encountered atheists who talk about "coming out" like homosexuals when they became more confident in their doubts, but just like a homosexual is not neutral about their sexual preference, neither is an atheist neutral about their belief in God or they would self-identify as agnostic. So why do atheists, whether unintentionally or surreptitiously, try to reposition as agnostics? I believe it is because atheism is indefensible.
Ask any intelligent atheist to prove God doesn't exist, and they will inform you the burden of proof is on the theist. An informed atheist might even mention Russell's teapot. Most atheists know it is very difficult to prove a negative, but as my friend Sarah explains here, this negative statement about God's existence doesn't shift the burden of proof to the theist, and asserting a positive philosophical statement is evidence the atheist does have a belief since you cannot hold a position without a belief.
An intellectually honest atheist must actively believe against every positive evidence for theism else they are not a rigorous atheist or not rigorously honest - take your pick. The atheist has a weak position from which to believe because one cannot prove nonexistence. In other words, there is no evidence for atheism, so the truthfulness and rigor of the atheist position hinges on negating every possible positive evidence of God's purported existence.
I had another atheist friend try to explain his "neutral" position by saying he didn't believe in the Easter Bunny or Santa Claus either. I had a good chuckle over that one. If someone cannot discern between the intellectual rigor behind arguments for the existence of God and belief in the Easter Bunny, I have to question their seriousness as a discerning truth seeker. I've had other atheists tell me they don't believe in Zeus, Apollo, or the other pantheon of gods and goddesses just like they don't believe in the God of the Bible. This is further evidence the atheist position is not neutral. This atheist is claiming active belief against all these other gods, but the "I don't believe in the Pantheon of Pagan Gods or your god(s) either" isn't any more compelling than the Easter Bunny argument. This is an inverse of the No True Scotsman fallacy or what I sometimes call the "tossing the baby out with the bathwater" argument.
I find the historical and philosophical arguments for God's existence quite compelling even when adjusting for my birth bias of being born in a Christian home. Most atheists I've encountered haven't investigated this evidence rigorously, and they seem to believe the only valid evidence for existence is physical evidence. This atheist belief is generally connected to the atheistic religion of Darwinism. I prove elsewhere in this blog that the preferred belief system of most atheists is Darwinism which I also argue as being a materialist "religion" that tries to eliminate God by substitution of "billions of years" in order to explain origins. 
I'm amazed by how many atheists seem incapable of discerning between credible intellectual arguments for God's existence and silly superstition while simultaneously castigating theists for being superstitious. At least I differentiate between a superstitious belief and a credible logical or philosophical argument for existence! And I wish more atheists would be honest about their "disbelief" actually being a belief system. I'm still looking for intellectually honest atheists who enjoy polite discourse, but they are very hard to find. After a few rounds they generally stop communicating or do what I'm now calling "Spontaneous Atheist Combustion"  where they get incredibly furious at me and lose all reason.
Atheist thought fascinates me because I'm very nearly an atheist myself. Out of the hundreds or even thousands of "gods" atheists say humanity has invented, I only believe in one more God than an atheist. I continue to believe in that one God because of the evidence. If the evidence is shown to be false, I would be compelled to stop believing as I hold truth as my highest value. I only ask atheists to do the same. Evaluate the evidence and inform your belief in whether or not God exists based on evidence. We call this critical thinking.
So what about agnostics? Generally, agnostics are atheists who are smart and/or lazy enough to recognize atheism is indefensible. Agnosticism is a safer position. You can basically stay out of the truth seeking endeavor by sitting on the fence and feigning ignorance on the question of God's existence. But, most self-identified agnostics I've met can't keep up the charade very long if you really engage them in a substantive conversation. Quite frankly, I don't think the label of atheist or agnostic is all that helpful once you're past the point of recognizing someone doesn't believe in the God who has Revealed Himself in the Bible. The God of the Bible claims to be the only God there is, so someone who is an atheist or agnostic is in some ways closer to the truth than someone who believes in a god or gods who are no more real than the Easter Bunny. At least the atheist has moved past superstition even if he tends to project superstition onto the theism position out of ignorance.
 For more information on origins go here.