Suppose that there is no God, that human beings are the highest beings relevant to our moral calculus (i.e., there may be aliens somewhere else that are higher than humans, but they don't morally matter). What, then, should one take as the highest aspect of human flourishing? Surely service to fellow humans. But service to fellow humans aims at an end beyond itself, namely our fellow humans' benefit. Now this benefit to our fellow humans cannot primarily consist in enabling them to serve their neighbor, or else the highest aspect of human flourishing consists in helping others to help others to help others ..., which results in vicious regress or circularity. Rather, in the end, our collective service to one another would have to be aimed at something else than service to one another. But if there is no God, then service to one another is the highest part of our flourishing. So it seems that if there is no God, the highest aspect of our flourishing consists in our promoting other, and hence lower, aspects of the flourishing of others. And that doesn't seem right.
Here's another way to see this problem. There is something paradoxical about pursuing the flourishing of others as our central end: what if we all achieved our end? Then our lives would lose what centrally gives them their meaning.
How does the existence of God change things? Well, our service to others in itself is not the highest human good any longer. Loving union with God is the highest human good, and service to others is valuable as it is partly constitutive of one's own union with God and promotes that union for others.