You treat the purpose given by a creator as extraneous or arbitrary, something the creator just "made up" for you and imposed on you, but in fact his purpose would be part of the very created thing he would create, not at all subjective but the very definition of objective. {Leaving the hypothetical for the Christian context for a moment, If we are made in the image of God, some part of us is always seeking God. It's part of us, it's not imposed on us. It's complex because of the Fall, which buried this part of us that seeks God and brought out our own desire to be little gods lording it over life, which I add merely to explain why we often don't experience this yearning after God, or we misapply it in the wrong directions.}
And why shouldn't we give the 'purpose' as purely arbitary? And, what is that 'purpose'? How do you know what that purpose is?? (and I am not talking about quoting some book).
It appears to be that trying to claim that the purpose is objective by defintion is not a very convincing arguement at all. It is entirely subjective.