The Atheist Perspective
The nature of the world, human beings, and social systems, combined with the universal human desire to live a fulfilling life.
This is formally demonstrated in Richard Carrier, "Moral Facts Naturally Exist (and Science Could Find Them)," in The End of Christianity, pp. 333-64, 420-29. For further discussion, see Moral Ontology and Goal Theory Update and Richard Carrier's Sense and Goodness without God.
Comments
Your naturalist viewpoint claims that nothing exists other than the particles that make up the natural world. As all particles interact in completely deterministic ways, the naturalist maintains that all thoughts and actions are completely predetermined in the same manner that the motion of the planets is, or the weather for example.
As such, it's utter nonsense for a naturalist to talk about "meaning" (importance, purpose) since the particles have no purpose, no goal, nothing, they are just particles interacting in a deterministic manner. The naturalist claims that the human is merely a collection of particles, without purpose or meaning, without free will. Nothing more than a slightly more biologically complicated flower.
see: http://www.richardcarrier.info/naturalism.html
Obligation: "A social, legal, or moral requirement, such as a duty, contract, or promise, that compels one to follow or avoid a particular course of action"
You might claim that "morality" can exist in the absence of theism if you define morality as the majority view point of what is right and wrong. Of course you can't claim that "objective morality" can exist in the absence of theism (objective meaning that a certain thing is morally wrong regardless of your view on the issue).
But, you haven't said where the obligation (requirement) arises, the best you can do is claim that "well, if you don't behave in a manner that the majority of society considers moral, the majority of society will consider you immoral". That's doesn't build the case for a moral requirement.
And, of course, your entire argument is a non-starter as you don't believe in free will.