I have also suspected he killed her based on his lack of emotion and lack of remorse and the fact that he dehumanized her by referring to her to LE as "it". But mostly I, too, suspected murder because he fled when he believed that she might soon be found because of the discovery of the pacifier. And that he took a gun and wasn't afraid to shoot at people, that makes him seem like he was capable of ending a life.
It seems that when parents kill their kids it is often for selfish motives. They want a different lifestyle, or have a love interest who doesn't want kids, or they feel like it's too much of a burden.
In MG's case, his daughter had special needs and, from an outside view, it did actually seem overwhelming to have to wake up with a baby every two hours indefinitely. Babies can be challenging as it is. (But we love them so much it doesn't matter.) His daughter presented extra challenges. Maybe too much for him.
Also, it seems that there were issues between him and his wife since they kept breaking up and we're living apart. Maybe he preferred that arrangement, but she wanted to be together as a family. Maybe he thought if the baby were gone, they could break up and he wouldn't be tied to her for the rest of his life through Ember. Maybe the fact that his wife was moving back in with him the next day made him suddenly feel trapped and pushed him over the edge. Maybe he just wanted a way out.
Also, he did not have a job and lived in a trailer with no running water. The idea of supporting a child and wife in those conditions might have seemed impossible and unappealing. Maybe that was too much responsibility for a guy who would prefer to hang out by himself and get stoned. Did he see a way to improve his life and the lives of the baby and his wife? Maybe the whole felt hopeless.
Just some guesses. It is really hard to think about as a parent. ;(
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