There are genes that spread rapidly in a population because they are highly inheritable and yet, once they spread, cause a population extinction. These are genes- they replicate easily- not anti-genes. An anti-gene is something that doesn't replicate at all: it kills off its organism in infancy, or makes it sterile. Each of them needs to develop entirely independently, because it can't be transmitted.

Note that in There is no Antimemetics Division, the anti-memes are persistent, independent entities, not information: they have an existence that is material, it's the information about them that cannot be communicated (it's an antimeme). So maybe a good starting point would be to ask ourselves what facts and patterns exists in the world that resist being noticed and communicated.

I think that was the starting point of author. Similar to “meme” the term is too broad on purpose, so you come up with different possible ideas depending where you started from