A large portion (I think it's the majority, but would be happy to be wrong) of our fellow man is a net loss to society, with some smaller percentage being a significant drain.

Giving more and more resources to those people does not make them magically more educated, productive, or congenial.

So it's not a "crabs in a bucket" mentality in that the greedy (which I assume means the wealthy here, as they're the ones funding the public system in the US specifically and the western world for the most part) are trying to keep the lower classes beneath them, it's that they are not interested in wasting their resources to no meaningful end other than increased consumption of low quality or worse goods and services.