As an empirical belief the idea that there is naturally a common morality is absurd. Many cultures around the world hold completely different beliefs regarding fundamental questions, the questions that rely on assumptions instead of reasoning. Are men and women equal? Is killing men always wrong? Do animals have rights? Should people be free? How does one derive the correct answers on these questions? Reason is of no help here. For example, there's no way to objectively prove that all men are created equal or that they possess natural rights. One has to take that as an unproven assumption. Some would hold that those two ideas are self-evident, but this is clearly wrong. Many people don't find them self-evident. Without an objective morality, there can be no right or wrong assumptions and therefore no immorality on any question. Murder can't be immoral, because you only think that based off of the assumption that humans have a right to their lives, and that assumption has no inherent validity.
You say that a lack of objectivity means that we need to think about our morals, but it's just the opposite. Moral subjectivity makes thought about morals impossible, or at least worthless. Something can only have worth in relation to an ideal. Imagine a test with no right answers. You couldn't be graded on it. There would be nothing against which to check your answers. None of your responses would matter. A poorly drawn smiley face would be as good as a 2 page essay. Similarly, when you've rid yourself of the notion of objective good and bad, there can be nothing to compare your morality too. There is no right or wrong morality. All moralities would have the same value and that value would be nothing. The belief that toppling stone walls on gays is alright would be as valid as the belief in gay rights. Pacifism would be just as valid as genocide. Objective morals give one the room for thought, in two directions. What is the objective principles to which I should adhere, and how do I apply them to my life?
Of course this is only relevant if we exclude the effects of atheism on moral thinking. Atheism leads to the same belief regarding morals but through a different channel. You say that society and genetics have a big influence under your atheism, but that's not what I said. Genetics and environment are the only influence under your worldview. There simply is no other input possible. You've made a big deal about how one needs to think rationally, but you fail to see how that would not be logically possible without God. Rationality implies the ability to choose. We can weigh the evidence in favor of two viewpoints and make a choice. Whether or not that choice is the one that is rationally correct is irrelevant. The important notion is that we can choose. Underlying the idea of choice is the notion that someone is doing the choosing. A rock can't make choices. Computers can't make choices. They are only heaps of matter, which are subject to the laws of physics. Humans can as our everyday experience shows, which means that there must be something transcendent of the material world in us, a soul. Since atheism rejects the soul it must also reject free will and therefore thought and rationality. If you reject thought in general, you must reject thought about morality.
Atheism implies a lack of free will. Morality only has value in a world with free will. It is a framework for deciding which is the right path to take. If one doesn't choose one's path, there is no need for morality.
Topic: Is evil nurtured, or natural?