Instapundit links to a study that finds a connection of some sort between owning cats and schizophrenia, the online journal is sciencealert.com. Some believe the link is a parasite called Toxoplasma gondii which infects both cats and humans who live with cats.
For what it is worth, my theory is that cats' natural behavior resembles that of sociopathic humans. This makes them more attractive in the eyes of people with some mental disorders, many of whom are women.
Don't get mad, it's just a guess.