Yea, I’ll give you some arguments for the view I think you want to support…
A bit of clarification first, though. The term “existential nihilism” is odd. The only thing all “existentialists” have in common is a focus on concrete existence—i.e., a focus on the world as it actually is. And a “nihilist” is just someone who denies anything like meaning/purpose/value, in some domain. That makes the term “existential nihlism” really odd, because I don’t think there has ever been a philosopher who thought that nothing about the world as it actually is, is value-less or purpose-less (i.e., nihilism).
Most nihilists are only nihilists because they think there is no transcendent meaning/purpose/value. IOW, nihilists generally recognize that things like food and water are valuable to you as the kind of creature that you are, they just think that those things are not “Really” valuable—not transcendentally valuable.
So basically, an “existential nihilist” is someone who denies any meaning/purpose/value to concrete existence. And that’s a view that is almost unsupportable, given that you have all kinds of basic biological functions, and act in the actual world as if it was filled with purpose/value—like getting food and water. I don’t think an “existential nihilist” is someone who would live longer than a day or two after they adopted their position.
Ironically, the only people who might be “existential nihilists” are the hardcore ultra-religious, who deny any meaning/purpose/value to actual existence only because they place all meaning/purpose/value in God’s world—some transcendent realm.
You probably just want to be a nihilist----a good old fashion nihilist—someone who denies there’s any transcendent meaning/purpose/value to actual existence.
Anyways, you already mentioned one way of arguing as a nihilist----that “incredulity” stuff. You might say that all statements about value or ethics use properties that do not actually exist—and thus all statements about value/ethics are systematically false. Or you might argue against any transcendent source of value. E.g., you might argue that all morality requires a perfect God, but a perfect God doesn’t exist, therefore neither does morality.
Arguing for nihilism like above is just a game of whack-a-mole. You wait for someone putting forth a view about meaning/purpose/value—and then you whack it away. That seems to be the most common----since trying to have a positive argument for a negative thesis (like nihilism) is hard to do.
One really famous argument for nihilism comes from Nietzsche’s genealogical method. Basically Nietzsche tells a story about the origin of morality. He thinks that morality arose out of different groups struggling for power, and more specifically it originated because the weakest group—the one with the poorest standing in terms of existence-based values—posited a new kind of otherworldly value in order to lord it over others, gaining power over them. “Hey guys, why do you think cars and women are so good? Isn’t an eternity of bliss better?” – “Ok sheesh yea, are the Church membership fees due quarterly or what?” I won’t go into the story—that’d take to long—but the general gist is that the historical origin of morality makes it highly unlikely that the otherworldly values that were posited actually exist.
Here’s an analogy: Suppose I really need money (or power). I don’t have money, (or power). But I tell you that I’ve discovered an amazing cure-all product that you need to buy, for big bucks. I tell you it cures everything. The upshot of what Nietzsche is saying seems to be that the fact that I have so much to gain gives you a reason to doubt the truth of the claims I’m making.