Cariis, this is a simple answer.
He knew it could be proven that he killed his wife. The evidence would be there. His DNA under her fingernails. His prints around her neck. That could be proven.
But after dumping his babies in oil, which I fully believe was done intentionally to erase evidence, he believes there won't be evidence of who killed them.
So why not say his wife did it?
This guy isn't a complete imbecile (dunno why people keep saying that), however, he's also not the sharpest tool in the shed. I remember watching a show where a former DA made a comment: "Murderers are idiots". Even when they think they can't be caught, they can be. And they'll lie and lie and lie, even when the evidence proves they're responsible. It wouldn't be the first time someone would lie about killing one person but not another (and it later proven they killed both). His confession is meant to give him a defense. Instead of being a cold-hearted monster who killed his girls and his wife, he can be the hero who killed the murderer of his children by telling this lie.
And if there's anything I've learned with pathological liars, they do tend to put truths in with their stories. It makes them more believable.