This student is considering the “punishment” handed down to the killer-father, and trying to figure out what the judge might have been thinking.
We can see the problem with motif/motive. We might speculate that the student was suggesting a pattern of behavior in the father that preceded and included the murder, a recurrent concern or desire that had motivated other (less lethal) actions in the past. More likely, alas, is that the student either didn’t know how to spell “motive” or typed “motiv” and was “helped” by Spellcheck to choose “motif” as the correction. The error is merely a spelling mistake, or perhaps a bad word choice.
But the real interest in his sentence is the new phrase “bettering off.” In the case in question, evidently the father felt his son would be “better off dead” than addicted to drugs. “Better off” is a common phrase modifying so many choosers: You’d be better off saving your money. You’ll be better off without him. You’d be better off with a college degree. Etc.
In the sentence the student had already begun, though, “better off” doesn’t come in naturally. Unwilling to start the sentence over, he plows on, determined (like Cinderella’s sisters contemplating the glass slipper) to “make it fit.” He creates a verb, “to better off,” and then uses its present-participial form as a gerund. Why not?
With this new verb much becomes possible. Its superficial resemblance to “butter one up” is one step toward normalization. “When he gives you presents you think he’s trying to better you off, but he’s only buttering you up.”
This verb is going to enter my lexicon, as “to unfair against” already has. It’s a living language, after all, right?