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I think it's equally likely that they want to commit suicide but don't want to abandon their families.
I'm not saying it's definitely the reason, but it doesn't strike me as being especially illogical or dependent on a male sense of entitlement.
Also what about all of the mothers who kill their children? What's their rational? Will fact check, but I'm pretty sure just as many women kill their children as men. Either way you've got to be in a pretty desperate place when that seems a viable option.
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The references I can find with a quick google put murder of children by a parent were "roughly" equal between fathers and mothers for US and Australia, with "roughly" doing a bit of heavy lifting (eg 40% mothers vs 57% fathers). The UK reference I found had no stats but said mostly fathers.
That's murder of children by a parent.
But family annihilators, the people who kill their children and the other parent as well, are almost always men.
Not sure I agree. It happens too often and it's almost always men doing it to women and children. So while there may be a mental health element, something in society is creating/enabling men prepared to do this when the crisis hits in a way that isn't happening to women.
Personally I think there's a sick sense of ownership in these men that makes them think they have the right to take "their" families lives.