He's not denying that the conditions exist. What he is denying is that they are illnesses. A more accurate term would be injury.
http://www.sciencedaily.com/releases/2012/08/120816170400.htmDoes a viral infection count as illness or injury?
(Note the numbers are very significant here: 10-20% of people carry the T. Gondii infection. People with T. Gondii infection are 7 times more likely to attempt suicide. -> 60% or more of suicide attempts could be T. Gondii-related).
Alternatively, perhaps the axioms of natural law dictate that T. Gondii is either (a) caused by child abuse or (b) imaginary. Ask the cult leader for the correct answer. Interpretations of natural law at this level are quite subtle.
Or perhaps cat ownership is child abuse?
http://healthland.time.com/2012/07/03/are-cat-ladies-more-likely-to-attempt-suicide/(In the mouse, infection causes a loss of cat aversion. Maybe a strong infection could turn you into a upstanding Statist? Keep your girls clear of the cat litter Myrkul.)
Did you read that paper? It has all the hallmarks of being an exaggeration or outright false positive.
1) It has no figures and only two tables. One has an obvious error indicating inadequate peer review. Nowhere is the actual data shown.
2) Main source of data is reported to be "severely skewed and bimodal"
3) Much larger effect size than expected due to previous literature. Implausible effect sizes are a trademark of false positives.
4) Strange, unequal sample sizes indicating they were likely not determined beforehand and high probability that sequential sampling occurred.
5) They actually admit to making multiple comparisons, but do not correct for this before making inferences.
6) Control group and Suicide group exclusion criteria vary greatly. The effect of this is not assessed.
-What is the toxo antigen they used? Could there be a human gene the antibody to it also reacts with that is upregulated by SSRI, etc treatment?
Also, you have misinterpreted odds ratio as a risk ratio, and the claims you make don't make sense on the face of it: google says about 33% of US households have at least one cat while attempted suicide rates are close to .1% of people.
Anyway, if there actually was strong evidence that having a cat lead to your children having mental disorders later in life, I think it would widely be considered as child abuse.