Zero Sum

“It wasn’t great for everyone, therefore it wasn’t great at all.”

“America wasn’t always great for everyone, therefore it was never great at all.” 

This seems fallacious to me, like some sort of zero sum fallacy or something. Is that accurate or am I in the wrong here? 

Your intuition is correct; the statements you've provided exhibit logical fallacies, primarily relating to the concept of zero-sum thinking, although it's a bit more nuanced than that. Let's break it down:

### Zero-Sum Fallacy
The zero-sum fallacy is the belief that one person's gain is necessarily another person's loss, implying a fixed amount of resources or benefits such that any increase for one group must result in a decrease for another. In the context of the statements you provided, zero-sum thinking is not directly applicable because the statements are not about the distribution of resources but rather about the overall evaluation of "greatness."

### False Dilemma
The statements can be seen through the lens of a false dilemma (also known as a false dichotomy). This fallacy occurs when someone presents only two options or outcomes in a situation, neglecting other possibilities. In this case, the statements imply that there are only two possible states regarding America's greatness: either it is great for everyone, or it is not great at all. This ignores the possibility that America can be great for some aspects and populations while still having significant flaws.

### Perfectionist Fallacy
Relatedly, the perfectionist fallacy is at play here. This fallacy dismisses any measure of success or progress if it is not perfect. The statements suggest that unless America's greatness is absolute and without exception, it is not great in any capacity. This ignores real-world complexities and the idea that a nation can have a mix of successes and failures.

### Hasty Generalization
Additionally, there's an element of hasty generalization. This fallacy involves making a broad generalization based on a limited amount of evidence. Stating that America was "never great at all" based on the fact that it wasn't great for everyone generalizes the entire history and achievements of the country from specific negative examples without considering the full spectrum of experiences and contributions.

### Cognitive Biases
1. **All-or-Nothing Thinking**: This is a cognitive distortion where situations are viewed in black-and-white terms, with no middle ground. The statements reflect all-or-nothing thinking by failing to recognize that America's history and status involve shades of gray.
2. **Negativity Bias**: This bias means that negative experiences have a more significant effect on one's psychological state and perceptions than positive or neutral experiences. The statements may be influenced by focusing more on negative aspects, thus discounting the positive ones.

### Summary
To accurately evaluate the greatness of America (or any entity), one must consider a nuanced, multi-faceted view that acknowledges both achievements and shortcomings. The statements you provided oversimplify this complex issue by falling into logical fallacies like false dilemma and perfectionist fallacy, thus presenting a skewed perspective. So, you're correct in recognizing that the reasoning behind those statements is fallacious.