It starts by assuming an initial difference between right and wrong, with truth being, as you suggest, "a moral position...that is right and just," and a lie, being "an immoral position...which is "wrong and unjust." However, there is no base difference between a truth and a lie, and the only reason either of you make that distinction is that it's something you've been taught since you were five.
Based on the actions and reactions of humans, as studied objectively, it is possible to determine behaviours which are universally preferrable and behaviours which are universally unpreferrable. Taking it one step further, we discover that all humans have terms that are consistently used to describe the difference between these behaviours, just as birds have calls to describe different states in their mating habits. Thus we may fairly equate the human english term 'good' with universally preferred behaviour, and the human english term 'bad' with universally unpreferred behaviour.
Remember that we did conclusively prove that preferred behaviour does exist. And here we have shown that preferred behaviour is recognized and understood by all humans. Thus for you to say that the distinction is made subjectively is false. All humans make the distinction in the same manner, with the exception of psychopaths.
The preference of truth over falsehood expressed in making the proposition does not imply that there's a fundamental difference. If speech made something either true or false, I should say that there is no such thing as "nothing", because in naming it, I have found something to describe. Therefore, there is no such thing as nothing. Again, poor logic.
No, the logic in the statement I put forward was perfectly valid. It is your logic that is self contradictory and therefore false:
'The preference of truth over falsehood expressed in making the proposition does not imply that there's a fundamental difference.' In making this statement you assert that I am incorrect, that my statement is untrue. If there were no fundamental difference between truth and falsehood there would be no reason to ever make such a statement, because you would already agree with me. If there is no difference between something that is true and something that is false then there is no reason to debate, or indeed communicate, because everything anyone ever said about anything would have no value. We would be unable to say 'yes that sounds correct' because correct and incorrect would have no definition.
To assert, as you are asserting, that there is no difference between true and false is to assert that your statement is in-fact true and therefore not false, and in the action of doing this you destroy your own proposition!
Further, if you do not believe in God, how can you create a law of good and bad that apply only to mankind? It is only in religion that we are the divine race, deserving of the special attentions of the world. In science, we're highly evolved monkeys, and therefore, to create an idea that - as you said, is only applicable to the relations of humans - is to suggest that nature created right and wrong just for us. For, you say aggressive force is immoral: if so, how is the lion excused from killing a gazelle? Why should it apply only to humans, if you do not believe we are governed by higher laws?
You reject the definition of morality, of the debate, in making this statement. Morality only exists between humans. Therefore all counter-arguments as to how it might be applied to animals or ... matter are void. If it is between animals (and not humans) then it is not morality and hence you are no longer debating within the scope of the subject of the debate.
But, granting a concession for the freedom to explore your proposition further, let us examine what you have asked:
"For, you say aggressive force is immoral: if so, how is the lion excused from killing a gazelle? Why should it apply only to humans, if you do not believe we are governed by higher laws?"
Why should the laws of physics only apply to physical reality? Why should biology only apply to animals? Why should mathematics only apply to symbols on paper?
Why would physics apply to someone's dreams? Why would biology apply to inorganic matter? Why would psychology apply to the nuclear processes of atomic fission?
To answer your question: Morality only applies to humans because that is the scope of its study and application.