Can objective morality exist in Atheism?

[objectivitees]

You cannot have an objective right and wrong anywhere.

Then how do you (Atheism) rationally justify making a moral claim?

It is a principle on which morality is based,...

Ok, buy why is that "principle" valued as opposed to one that says, "do unto others before they do unto you?" (the selfish rule)

but the morality itself is subjective. The only thing it reinforces is surviving and procreating as a species. The golden rule is instinctive.

This is an equivocation making "survival" and "golden rule" the same thing, and serves only to muddy the issue you are trying to explain. If 'survival' is the goal, again I ask why? Why not adopt a value that says kill them and take their food? Why is the 'golden rule' chosen as opposed to the selfish rule?