When designing a game, "The game is fun," is a shitty razor because it doesn't tell you how to prioritize or make trade-offs. "Multi-player is the most fun mode," is a better razor because if you're trying to decide which features to cut, the single player ones are clearly it.
"Anti-value" is, I think, another way to say something similar.
This touches on a cognitive mistake I see often. We often naturally think of choices in terms of "yes or no". Do I want to go out for dinner tonight? Should I ask that person out? Should I buy that house?
But opportunity cost pervades all aspects of life. Our time and resources are finite and any "yes" choice is implicitly a "no" to the other options that give up the capacity to say yes to. It's very hard to make good choices without thinking of those other options.
Framing your values in terms of "razors" or "anti-values" is a good way to get out of the "yes/no" mindset and into the more accurate "which one" mindset. It helps you discriminate among options.