When logic gets twisted to suit one's needs, as in making what one wants to believe seem true or an illogical choice seem rational, that's called rationalizing. You can see some great examples of this here in a comically titled piece, 'Atheism Logical?' It's full of what I guess passes for logic when you need to create some self-satisfying reasons for not just justifying your indulgence in religious belief but also to put down atheists who don't fancy such an indulgence. Below are some really embarrassingly silly arguments from that piece which I just want to quickly address...

"Before we edited God out of the schools..."
Without explaining how removing violations to the Establishment Clause is responsible for the social ills you describe, one could pick anything from around that time and say they are responsible. For instance you could say "before we went to the moon..." or "before the civil rights movement" or better yet, "before we forced god into our Pledge and onto our currency..."

"When it comes to science, the evidence is that creation was created."
Actually no, there's no scientific evidence for the universe being a "creation" nor for any creator, and Einstein himself could have said the universe looks like a creation but that wouldn't make it so.

"The truth is that if people really want to do something, they find a way to justify it."
And one of the greatest ways to justify something is to use the Christian bible. It's been used to justify wars, enslaving people, denying equal rights, and a host of other infamous things.

"missionaries risked their lives to tell the various tribes about God"
There was a story I remember from school about British missionaries in the South American rainforest appalled by the lack of clothing the indigenous people had. They told them that was immoral and not what god wants and got them all nice, hand knitted sweater. The tribe liked them so much they wore them all the time. They naturally got soaked from the rain, and wearing soaking wet sweaters all the time made them all come down with pneumonia. Praise god!
You might also like this book, 'Don't Sleep There Are Snakes'

"The problem is that without God, morals are always subject to change"
As they are with religious belief as well, as shown above in the various atrocities which used to be justified by invoking your god (and sadly some still are).

"The problem with atheist morality is that it tries to use values from the Bible and yet remove the power of God from the equation."
And the problem with Christian morality is it tries to use pre-existing moral values but then taints and perverts them like how it ruined the Golden Rule, removing empathy from the equation. Furthermore, it doesn't actually teach an understanding of why something is moral or not, but merely attempts to train people as you would a dog by directing a series of desired actions followed by a promise of a reward for doing them and a punishment for not doing them (ie - the power of God). How about the power of understanding? The power of empathy? I think in there lies true power.