Having known some people that fit into this category, I don't think anybody has claimed that they are depressed or anti-social. The primary claim is that they're nuttier than a bloody fruitcake.
'Crazy cat ladies' are not a thing, study finds - CNN 'Crazy cat ladies' are not a thing, study finds
"We found no evidence to support the 'cat lady' stereotype: cat-owners did not differ from others on self-reported symptoms of depression, anxiety or their experiences in close relationships," the study said.
"Our findings, therefore, do not fit with the notion of cat-owners as more depressed, anxious or alone."