Why are athiests angry at God?

They're not. If they say they are, or if it appears that they are, then their anger is simply misdirected. Coping mechanism. You ever get really angry at another person, and go punch a hole in a section of drywall? Usually, we do this to cope with our anger towards the person because we know better than to assault a person. But it's misdirected anger because logically we should be assaulting the person and not taking it out on inanimate structures.

In the case of being 'angry at God' you would be right to assume that it doesn't always have to be related to anger towards another person. However, it can be easier to direct hate towards God than to admit that you hate your life or that you hate the nature of reality. So I mean, God could still have a use in a post-religious world as an intellectual punching bag of sorts. This is no reason to believe in His existence.

There is an equivalent to this that stands out, and it is addressed in the video I recently posted on fallacies. The good old 'straw man', where we erect a misrepresentation of another person's actual position because it is far easier to tackle a position we made up ourselves than it is to tackle what the person has actually said.

This brings me to wonder: Why is there so much appeal among Christians trying to be reasonable that they would say they Hate the Sin, Not the Sinner?

Is it really because only God can judge as they may say, or can it be chalked up to a deeper issue - maybe that because Christians who according to their own beliefs must also be classed as sinners.... when this fact is so plain and simple... it is no longer so easy judge another for being a "sinner," but rather than get rid of the concept of sin entirely because they have to address the problem of evil somehow, stop hating the sinner and just hate the sin? Mosaic law said to stone an adulteress. Jesus said let he who is without sin cast the first stone.

I'd also like to see the original source cited, and I can't find a link from the article that this article links to.

I did come across the source of the study guys, however it costs $11.95 to view.

Here is the abstract summary, and I'll post the link below it.

Anger toward God: Social-cognitive predictors, prevalence, and links with adjustment to bereavement and cancer.
By Exline, Julie J.; Park, Crystal L.; Smyth, Joshua M.; Carey, Michael P.
Journal of Personality and Social Psychology, Vol 100(1), Jan 2011, 129-148.
Abstract
Many people see themselves as being in a relationship with God and see this bond as comforting. Yet, perceived relationships with God also carry the potential for experiencing anger toward God, as shown here in studies with the U.S. population (Study 1), undergraduates (Studies 2 and 3), bereaved individuals (Study 4), and cancer survivors (Study 5). These studies addressed 3 fundamental issues regarding anger toward God: perceptions and attributions that predict anger toward God, its prevalence, and its associations with adjustment. Social-cognitive predictors of anger toward God paralleled predictors of interpersonal anger and included holding God responsible for severe harm, attributions of cruelty, difficulty finding meaning, and seeing oneself as a victim. Anger toward God was frequently reported in response to negative events, although positive feelings predominated. Anger and positive feelings toward God showed moderate negative associations. Religiosity and age correlated negatively with anger toward God. Reports of anger toward God were slightly lower among Protestants and African Americans in comparison with other groups (Study 1). Some atheists and agnostics reported anger involving God, particularly on measures emphasizing past experiences (Study 2) and images of a hypothetical God (Study 3). Anger toward God was associated with poorer adjustment to bereavement (Study 4) and cancer (Study 5), particularly when anger remained unresolved over a 1-year period (Study 5). Taken together, these studies suggest that anger toward God is an important dimension of religious and spiritual experience, one that is measurable, widespread, and related to adjustment across various contexts and populations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)

Link: http://psycnet.apa.org/index.cfm?fa=buy.optionToBuy&id=2010-26912-003