This is a question I've heard from skeptics and atheists. The notion is that if we can understand the world around us without God then why believe in God? Or to put it another way, why is God necessary to understand our existence?
I know why God is necessary for me but I have a hard time giving a meaningful answer to someone who asks this question since so much of it is wrapped up in my personal experience. I'm not looking for convincing reasons or logical proofs for the existence of God, since I ultimately think those are an exercise in futility.
What would the Orthodox answer be to a question like this? Or at the very least, why should one consider God?
Quite simply, without God, our foundational values undergo revaluation as well. Our understanding of right and wrong, good and evil, is heavily rooted in our understanding of God and our relationship with God. God is the perfection of Goodness; goodness, virtue, wisdom, etc. obtain their value insofar that they are similiar those of God. The degree of something being evil is determined by how much it is a deviation from the Good.
Many secular humanists in Britain and America (in particular) essentially advance that we can expunge God and Christian "superstition" and be all the better people for it. They generally do not acknowledge, however, that things like natural rights and absolute values (e.g. integrity, humanitarianism, self-sacrifice--i.e. being the hero, for the sake of humanity, etc.) and disvalues (e.g. egoism, hypocrisy, murder, genocide, rape, etc.) become more or less subjective and arbitrary when divorced from God, or from an objective standard.
Also, God gives greater credibility to free will, which is foundational to how we approach law and societal order. Atheists who do not believe in God or gods generally reject any kind of dualism between the material and the spiritual; they only believe that exists which can be discerned through the senses. It is for this reason that skeptics and atheists cannot well explain how free will is possible within a materialist metaphysic. As a tidbit, several months ago I read a popular scientific article which states that researchers have discovered human free will in the brain. It goes on to explain how the brain has a process of weighing decisions. The unstated fact in the article, however, is that this process and the decisions made are the outcome of chemical reactions in the brain, without variable outcomes given the same conditions.
Several philosophers and writers (e.g. Nietzsche and Camus) have addressed the implications of life devoid of God and religious belief in the afterlife. They offer insights that many popular atheists tend to gloss over.