He is saying that "living in accordance with nature" is a nonsense concept. Nature is boundless indifference and by your very existence, by your very desires, you are not and can not live in accordance with it. And beyond that, the Stoics are taking their view of the world and are projecting it onto Nature.
One of the things Nietzsche hated most were life denying philosophies. If your philosophy of life made you weaker, then it was evil. He considered Stoicism a philosophy that made you weaker by accepting what was. For example:
From the article: “Starting with things of little value—a bit of spilled oil, a little stolen wine—repeat to yourself: ‘For such a small price, I buy tranquillity.’ ” Nietzsche would ask if you are buying yourself tranquility because you want to? Or because you are too cowardly to say something? Based on how I read the article, the latter is almost definitely true.
> One of the things Nietzsche hated most were life denying philosophies. If your philosophy of life made you weaker, then it was evil.
I'm not sure I entirely agree with this. I think that Nietzsche observed philosophies and decided some that thought they were life affirming were life denying, but I don't necessarily think built into that is hatred. Indeed, I think you can take out of Genealogy that he rather admired the slaves. Their life denying philosophy served their ends, after all.
I actually think Nietzsche probably has more in common with the Stoics than not. They both seek to overcome a world that might deny them. One through acceptance, one through self-overcoming.
One of the things Nietzsche hated most were life denying philosophies. If your philosophy of life made you weaker, then it was evil. He considered Stoicism a philosophy that made you weaker by accepting what was. For example:
From the article: “Starting with things of little value—a bit of spilled oil, a little stolen wine—repeat to yourself: ‘For such a small price, I buy tranquillity.’ ” Nietzsche would ask if you are buying yourself tranquility because you want to? Or because you are too cowardly to say something? Based on how I read the article, the latter is almost definitely true.