It seems that the previous studies were finding relationships based on biased data. Many of the studies were retrospective, meaning they asked participants to look back on their lives and recall habits, living situations, and health issues. Recall like that is fairly unreliable, though, and with small sample sizes on top of the bias issues the resulting data wasn't exactly optimal. Some studies also failed to control for confounding factors, like occupation, socioeconomic level, other pet ownership, and over-crowding in the home. A few or all of those factors may be the true culprits. In some of the analyses that the University College London group performed, they found a link between cat ownership and mental health problems when they only looked at those two factors. The link disappeared once they controlled for confounding factors, which implies that cat ownership is correlated with some other factor that's actually causing mental health problems.