If you have an hour, this video by Ravi Zacharias explains pretty well the philosophical inconsistencies of atheism.
His focus is on three main areas:
Morality: Atheists have no source for a transcendent morality. When you believe that humans are simply evolved animals, then we have no more basis for morality than animals do. Some atheists do realize the implications of the statement “God is dead”. What do you replace Him with?
Meaning: Atheists can have no more than a superficial meaning for life. There is no ulimate point of reference for meaning.
Hope: There is no hope. In an atheist’s worldview, we all die, and humanity dies too, and the universe expands to a cold lifeless space. There is no afterlife.