Though I generally agree with your hypothesis, I think that there is something you ought to make more clear. Namely, that religion is not a necessary condition for infanticide.
I agree completely, however I think that non-religious infanticides happen much more rarely than religiously motivated ones.
You asked streetapologist to provide an example of either "1) a mentally ill atheist mother who killed her children, or 2) a mentally ill religious mother who killed her children due to a non-religious motivation". In the realm of mental illness, I can think of two disorders off the top of my head that don't involve delusions or any sort of psychosis that would lead to the same outcome; postpartum depression and Factitious Disorder-by proxy (formerly Munchausen's Syndrome-by proxy).
Again, I agree completely. But how many non-religious, contemporary examples can we find, especially compared to the examples I have already posted on that do involve religious motivation? The only argument I made was that religion serves as a catalyst for infanticide, and non-religious examples will be much more rare, and accordingly, harder to find.
Varkam then provides a non-religious example of infanticide, but upon closer inspection, it is actually an argument for my side:
I believe that Brooke Shields recently came out in the open regarding her postpartum depression (and was subsequently blasted by Tom Cruise-religious nutball and actor-about her seeking treatment in the form of therapy and SSRIs) during which she recounted a tale of how she almost killed herself and her baby as a direct result of the depression.
Brooke Shields admitted that she, like many thousands of women, experienced infanticidal and suicidal feelings due to post-partum depression. And like many thousands of women, her feelings were not religiously motivated. But also, like many thousands of women, Brooke Shields never killed her kid! Brooke Shields did not have sufficient legitimization for her feelings, and instead she recognized the disease for what it was. She talks about it, rather than acts on it. This is no example of non-religious infanticide at all. Brooke Shields has not met the requirements for membership in The Offspring Murder Club.
But what if Brooke Shields did have intense religious feelings during that time? Would she have done the same thing as Offspring Murder Club member Andrea Yates, who was suffering from 1) severe postpartum depression, and 2) severe afterlife-belief?
Factitious disorder-by proxy is a little more exotic. With respect to this conversation, mothers who are afflicted will create illness or injuries in their children for reasons other than secondary gain. There have been several documented cases of this over the years, including ones involving mothers eventually killing their children. Have you seen the movie The Sixth Sense? There is a character in that movie who kills her daughter in this fashion. I'm not offering that as evidence, only an illustration.
Again, I agree with Varkam, although it would be nice to have some actual examples of this disorder to look at.
Suffice it to say I think that you are on the right track when it comes to religion. It is true that not all religious people commit these acts, but the word catalyst fits very nicely.
Well, Varkam and I agree about 95% of the time. I appreciate his input. But as far as Brooke Shields goes (and all other post-partum depression sufferers who don't kill their babies), they belong in my evidence bin.
The afterlife can be hazardous to your children's health.