I was always puzzled how these cats actually fed. These sabre toots seem to get in the way of feeding and chewing.
The theory is that the sabre-tooths evolved to specialize in feeding on long-necked camelids (camel family) and the teeth evolved to let them deliver a fatal slicing bite to the neck. The sabre-tooths teeth fit neatly between the neck vertebra of a camelid, and have serated edges to let them slice through the tissue - the teeth are made for slicing, not stabbing (edit: as much as specialized stabbing).
Being so specialized they likely went extinct when their prey did (for whatever reason).