In my opinion it is not worth getting into interpreting the words too closely, it just means that the authors came up with some measures that demonstrated their tool is "better" than the competition.

But then the tool itself operates in a different way, so "better" or "worse" depends on what the goals are.

Here I suspect that they count how many pairs end up "broken" up because one of the pairs did not pass. Evidently, we'd want the fewest pairs to be broken.

But again fastp does something else than Trimmomatic; By default it trims right-to-left whereas Trimmomatic has a much stricter left-to-right operation.

That being said, fastp is a great tool and I would recommend it.