On first read, I thought it was something that neutralizes antibodies, rather than antibodies that neutralize the virus.
My layman's assumption was that the antibodies would always neturalize, so adding the adjectives threw me off the meaning.
Not all antibodies are neutralizing. Antibodies can only bind to a certain part of pathogens, but if an antibody binds to something it might not disrupt what that thing needs to do to infect the body. Relating this to SARS-CoV-2, it looks like if an antibody bind to something other than the spike protein, the virus can still infect cells. As another example, most people have been exposed to at least some other coronaviruses, and of that group, some of those people have developed antibodies that react to SARS-CoV-2. A recent paper [1] looked at if these "cross-reactive" antibodies were helpful in preventing COVID, but it looks like they're non-neutralizing as they couldn't see any effect.
0: https://blogs.sciencemag.org/pipeline/
1: https://blogs.sciencemag.org/pipeline/archives/2021/02/10/do...