Absolute moral rules can be discovered through logical deduction.
Can you elaborate?
I don't believe that's possible unless you take an axiomatic approach which would obviously be a moral relativist approach since we can just disagree on the choice of axioms themselves and prevent any deduction.
How do you overcome the is-ought problem?
Just because its easy to get a bunch of humans to agree say murder is wrong, doesn't mean you can call that objective.
The reason humans and ants differ so much in morality is because of the difference in the subjective experience of being a person versus being an ant.
If morality is subjective, you'd expect creatures with similar subjective experiences to agree with each other.
You'd expect one subjective blob of rules to conform to human biology/sociology and a separate blob of subjective rules to apply to antkind with no real way to interface between the two.