It's just another woman crazy enough to murder her children. The 'whys' shouldn't even come into play here.
But of course, they will.
I agree, your mentally ill if you kill your own children. It doesn't matter if it's a home school mother, or a public school mother. The Mentally ill do not need very good (or usually have) very good reasons for doing what they do, kind of like the media when they spin a story