Firstly if nihilism is just the rejection of on particular type of claim then it is not a position in and of itself. Secondly I did warn you that even if I indulged your definitions my actual argument would not actually change.
You have constructed a small box in which, definitionally meaning cannot exist. You have not done this by showing that what I most generally refer to as meaning doesn't exist but simply by refusing to accept any definition of meaning whatever, including yours effectively since you A won't define it and B can't demonstrate it.
The truth is I still find the idea of objective meaning self contradictory and you haven't shown how one can ever have meaning without some standard upon which we judge that meaning.
If you don't want to call humans caring about stuff meaning and you don't want to call humans caring for each other morality that is fine but whatever you call them they are enough. You haven't argued me out of caring and I don't take your "argument that nihilism is true" very seriously and not only because you don't actually believe it but also because it is a logically flawed idea to begin with.
Nihilism is true is a nonsense statement if nihilism is just the rejection of an unfalsifiable claim.
You know how I know? Because the same holds true for atheism. It isn't itself a claim, only the rejection of an unfalsifiable claim so it nonsensical to say it is true or false.
We should be evaluating the claims they reject to see if those are true or false.
IF you are alive and IF you care to continue doing so THEN you ought to engage in self care.
IF self care is worthwhile and IF some other organism contributes to caring for you THEN you ought to care for them right back as part of that self care in as much as no man (ant/zebra/wild dog/bee) is an island.
IF whether or not some person(s) contribute to your care is an unknown quantity (such as all humans who engage in a modern global economy) THEN all things being equal you should care for and about them to insure that care in every possible case.
This is equally true whether or not any objective morality exists.
This syllogism will still be true when you decide you are interested in having a conversation instead of stopping a conversation from getting too uncomfortable and confusing for you.
