Kitchen lines block from grease more than anything else. Grease goes down warm and liquid, cools in the pipe, and builds on the wall in layers until the bore narrows to nothing. It is a gradual failure that presents as a sudden one.
A cable machine punches through it and restores flow. Jetting scours the wall back to full bore and keeps the line clear considerably longer, which on a kitchen line that has blocked before is usually the better value.
Garbage disposals make it worse rather than better. Ground food adds solids to a line that is already coated, and disposal use is a common factor in repeat kitchen blockages.
Technician insight
Hot water and detergent move grease further down the line rather than removing it. It cools and deposits somewhere less accessible.